{
  "singular_order": {
    "order": "O_sing \u2245 Z_3 \u00d7 R_pair",
    "pair_factor": "R_pair = Z_3[eta]/(eta^2 - 3 eta)",
    "ideal_decomposition": "Every ideal of O_sing is uniquely of the form 3^a Z_3 \u00d7 I_pair."
  },
  "finite_levels": {
    "3": {
      "k": 1,
      "v7_chain_count": 2,
      "pair_ideal_count": 2,
      "total_ideal_count": 4
    },
    "9": {
      "k": 2,
      "v7_chain_count": 3,
      "pair_ideal_count": 7,
      "total_ideal_count": 21
    },
    "27": {
      "k": 3,
      "v7_chain_count": 4,
      "pair_ideal_count": 12,
      "total_ideal_count": 48
    },
    "81": {
      "k": 4,
      "v7_chain_count": 5,
      "pair_ideal_count": 17,
      "total_ideal_count": 85
    },
    "243": {
      "k": 5,
      "v7_chain_count": 6,
      "pair_ideal_count": 22,
      "total_ideal_count": 132
    },
    "729": {
      "k": 6,
      "v7_chain_count": 7,
      "pair_ideal_count": 27,
      "total_ideal_count": 189
    }
  }
}