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Properties

Label 3192.2.cu
Level $3192$
Weight $2$
Character orbit 3192.cu
Rep. character $\chi_{3192}(115,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $576$
Sturm bound $1280$

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Defining parameters

Level: \( N \) \(=\) \( 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3192.cu (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3192, [\chi])\).

Total New Old
Modular forms 1296 576 720
Cusp forms 1264 576 688
Eisenstein series 32 0 32

Trace form

\( 576 q + 4 q^{2} + 4 q^{4} - 8 q^{8} + 288 q^{9} + O(q^{10}) \) \( 576 q + 4 q^{2} + 4 q^{4} - 8 q^{8} + 288 q^{9} - 16 q^{11} + 32 q^{14} - 12 q^{16} - 4 q^{18} + 40 q^{22} + 36 q^{24} - 288 q^{25} + 20 q^{28} + 16 q^{30} + 4 q^{32} + 8 q^{36} + 60 q^{40} - 8 q^{42} + 32 q^{43} - 48 q^{44} + 4 q^{46} - 128 q^{50} - 72 q^{52} + 4 q^{56} + 16 q^{58} + 192 q^{59} - 20 q^{60} - 80 q^{64} + 16 q^{67} - 132 q^{68} - 12 q^{70} - 4 q^{72} + 68 q^{74} - 24 q^{78} - 108 q^{80} - 288 q^{81} + 132 q^{82} - 8 q^{84} - 72 q^{86} + 4 q^{88} - 112 q^{91} + 256 q^{92} - 144 q^{94} - 60 q^{96} - 32 q^{98} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3192, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3192, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3192, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)