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Properties

Label 3192.2.cz
Level $3192$
Weight $2$
Character orbit 3192.cz
Rep. character $\chi_{3192}(1787,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1152$
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.cz (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
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 1152 144
Cusp forms 1264 1152 112
Eisenstein series 32 0 32

Trace form

\( 1152 q + O(q^{10}) \) \( 1152 q - 10 q^{12} + 16 q^{16} + 10 q^{18} + 8 q^{22} + 20 q^{24} - 576 q^{25} + 20 q^{28} + 20 q^{30} + 80 q^{34} - 40 q^{36} - 52 q^{40} + 10 q^{42} + 36 q^{46} + 40 q^{51} + 28 q^{52} - 18 q^{54} - 48 q^{60} - 24 q^{64} + 56 q^{66} + 64 q^{67} - 12 q^{70} + 20 q^{72} + 76 q^{78} + 16 q^{81} - 4 q^{82} - 40 q^{88} - 152 q^{90} - 48 q^{91} + 36 q^{94} - 28 q^{96} - 32 q^{97} + O(q^{100}) \)

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

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