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Properties

Label 1232.2.ci
Level $1232$
Weight $2$
Character orbit 1232.ci
Rep. character $\chi_{1232}(221,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $640$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1232.ci (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1232, [\chi])\).

Total New Old
Modular forms 784 640 144
Cusp forms 752 640 112
Eisenstein series 32 0 32

Trace form

\( 640 q + 24 q^{8} + O(q^{10}) \) \( 640 q + 24 q^{8} - 12 q^{10} + 16 q^{14} - 20 q^{18} - 16 q^{20} - 40 q^{24} - 20 q^{28} - 40 q^{30} - 48 q^{31} - 20 q^{32} + 64 q^{34} - 24 q^{35} + 80 q^{36} - 40 q^{38} - 104 q^{40} - 8 q^{44} - 20 q^{46} + 80 q^{47} - 16 q^{48} - 24 q^{50} - 40 q^{51} - 36 q^{52} - 76 q^{56} + 4 q^{58} + 16 q^{59} + 16 q^{60} - 144 q^{62} - 24 q^{64} - 20 q^{66} - 24 q^{67} - 20 q^{68} - 172 q^{70} + 56 q^{72} + 56 q^{74} + 120 q^{76} - 200 q^{78} + 12 q^{80} + 320 q^{81} + 40 q^{82} - 80 q^{83} - 76 q^{84} + 32 q^{86} - 144 q^{90} + 16 q^{91} - 72 q^{92} - 48 q^{95} + 252 q^{96} + 12 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1232, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1232, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1232, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)