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Properties

Label 3192.2.e
Level $3192$
Weight $2$
Character orbit 3192.e
Rep. character $\chi_{3192}(1597,\cdot)$
Character field $\Q$
Dimension $216$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
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 648 216 432
Cusp forms 632 216 416
Eisenstein series 16 0 16

Trace form

\( 216 q - 4 q^{2} + 4 q^{4} - 8 q^{7} - 4 q^{8} - 216 q^{9} + O(q^{10}) \) \( 216 q - 4 q^{2} + 4 q^{4} - 8 q^{7} - 4 q^{8} - 216 q^{9} - 16 q^{10} + 16 q^{12} + 4 q^{14} - 12 q^{16} - 16 q^{17} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 200 q^{25} - 4 q^{28} + 16 q^{30} - 4 q^{32} - 4 q^{36} - 32 q^{39} - 16 q^{40} + 16 q^{41} - 24 q^{44} - 32 q^{46} + 216 q^{49} + 28 q^{50} + 16 q^{52} + 64 q^{55} + 28 q^{56} + 24 q^{62} + 8 q^{63} + 4 q^{64} + 64 q^{65} - 16 q^{66} + 24 q^{68} - 16 q^{71} + 4 q^{72} - 80 q^{73} - 16 q^{79} + 216 q^{81} - 40 q^{82} - 24 q^{86} + 16 q^{88} - 80 q^{89} + 16 q^{90} + 32 q^{92} - 16 q^{94} - 16 q^{97} - 4 q^{98} + O(q^{100}) \)

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

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