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Properties

Label 1232.2.cn
Level $1232$
Weight $2$
Character orbit 1232.cn
Rep. character $\chi_{1232}(141,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1152$
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.cn (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 176 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 1568 1152 416
Cusp forms 1504 1152 352
Eisenstein series 64 0 64

Trace form

\( 1152 q + 4 q^{4} + O(q^{10}) \) \( 1152 q + 4 q^{4} + 4 q^{11} - 32 q^{12} - 6 q^{14} - 20 q^{16} + 30 q^{18} - 18 q^{22} + 64 q^{24} + 124 q^{26} + 16 q^{29} - 48 q^{30} - 40 q^{34} - 24 q^{37} + 56 q^{38} - 40 q^{40} + 56 q^{43} + 26 q^{44} - 64 q^{46} + 288 q^{49} + 68 q^{50} - 112 q^{52} + 24 q^{53} - 28 q^{56} + 20 q^{58} - 24 q^{60} - 40 q^{63} + 28 q^{64} + 28 q^{66} - 40 q^{67} - 212 q^{68} - 24 q^{70} + 150 q^{72} - 88 q^{74} + 96 q^{75} - 256 q^{76} - 8 q^{77} + 8 q^{78} + 80 q^{79} + 176 q^{80} + 288 q^{81} - 160 q^{82} - 120 q^{83} - 110 q^{86} - 266 q^{88} - 312 q^{90} - 162 q^{92} + 84 q^{94} - 128 q^{95} - 184 q^{96} - 144 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1232, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)