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Properties

Label 3192.2.q
Level $3192$
Weight $2$
Character orbit 3192.q
Rep. character $\chi_{3192}(379,\cdot)$
Character field $\Q$
Dimension $240$
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.q (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q\)
Sturm bound: \(1280\)

Dimensions

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

Total New Old
Modular forms 648 240 408
Cusp forms 632 240 392
Eisenstein series 16 0 16

Trace form

\( 240 q + 8 q^{4} - 8 q^{6} - 240 q^{9} + O(q^{10}) \) \( 240 q + 8 q^{4} - 8 q^{6} - 240 q^{9} - 8 q^{16} - 16 q^{19} - 40 q^{20} + 8 q^{24} - 240 q^{25} - 40 q^{26} - 8 q^{36} + 8 q^{38} + 16 q^{44} - 240 q^{49} + 8 q^{54} - 24 q^{62} - 40 q^{64} + 32 q^{66} + 80 q^{68} + 80 q^{74} + 32 q^{76} + 40 q^{80} + 240 q^{81} + 64 q^{82} - 160 q^{83} + 96 q^{92} - 88 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3192, [\chi]) \cong \)