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Properties

Label 252.12.b
Level $252$
Weight $12$
Character orbit 252.b
Rep. character $\chi_{252}(55,\cdot)$
Character field $\Q$
Dimension $218$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 252.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(252, [\chi])\).

Total New Old
Modular forms 536 222 314
Cusp forms 520 218 302
Eisenstein series 16 4 12

Trace form

\( 218 q + 25 q^{2} - 1543 q^{4} + 18697 q^{8} + O(q^{10}) \) \( 218 q + 25 q^{2} - 1543 q^{4} + 18697 q^{8} - 1142299 q^{14} + 4412757 q^{16} - 17988550 q^{22} - 2098663646 q^{25} - 61458279 q^{28} - 115307276 q^{29} + 108998705 q^{32} - 885542404 q^{37} - 2132544602 q^{44} - 1754589898 q^{46} - 1042878870 q^{49} - 1190934811 q^{50} - 1914807148 q^{53} + 6621812869 q^{56} - 15640511854 q^{58} + 40598182313 q^{64} + 10384332432 q^{65} + 39492767152 q^{70} - 41128406466 q^{74} - 19537058476 q^{77} - 85322736240 q^{85} - 158793819106 q^{86} + 88648683642 q^{88} + 25006845506 q^{92} + 185077680881 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{12}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(252, [\chi]) \cong \)