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Properties

Label 1232.2.cu
Level $1232$
Weight $2$
Character orbit 1232.cu
Rep. character $\chi_{1232}(211,\cdot)$
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.cu (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

\( 1152 q + 4 q^{4} + O(q^{10}) \) \( 1152 q + 4 q^{4} - 4 q^{11} + 32 q^{12} + 6 q^{14} - 20 q^{16} - 50 q^{18} + 18 q^{22} - 16 q^{23} - 124 q^{26} + 80 q^{30} - 40 q^{34} + 24 q^{37} - 56 q^{38} + 30 q^{44} + 288 q^{49} + 80 q^{52} - 24 q^{53} - 64 q^{55} + 28 q^{56} - 20 q^{58} - 24 q^{60} + 28 q^{64} - 92 q^{66} + 40 q^{67} + 260 q^{68} - 24 q^{70} - 350 q^{72} - 100 q^{74} - 96 q^{75} - 8 q^{77} + 8 q^{78} - 176 q^{80} + 288 q^{81} - 80 q^{82} + 200 q^{83} + 98 q^{86} - 326 q^{88} - 320 q^{90} - 154 q^{92} - 140 q^{94} - 200 q^{96} + 16 q^{99} + O(q^{100}) \)

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

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