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Properties

Label 1176.2.t
Level $1176$
Weight $2$
Character orbit 1176.t
Rep. character $\chi_{1176}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1176.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1176, [\chi])\).

Total New Old
Modular forms 480 160 320
Cusp forms 416 160 256
Eisenstein series 64 0 64

Trace form

\( 160 q + 4 q^{2} + 4 q^{4} - 20 q^{8} + 80 q^{9} + O(q^{10}) \) \( 160 q + 4 q^{2} + 4 q^{4} - 20 q^{8} + 80 q^{9} + 18 q^{10} - 16 q^{11} - 4 q^{16} - 4 q^{18} + 28 q^{22} + 18 q^{24} - 80 q^{25} + 30 q^{26} + 8 q^{30} + 14 q^{32} + 8 q^{36} + 18 q^{38} + 30 q^{40} + 32 q^{43} - 40 q^{44} + 4 q^{46} - 104 q^{50} - 36 q^{52} - 16 q^{57} + 18 q^{58} + 96 q^{59} + 14 q^{60} - 128 q^{64} + 36 q^{66} + 40 q^{67} - 96 q^{68} - 10 q^{72} + 24 q^{73} + 46 q^{74} + 36 q^{78} - 36 q^{80} - 80 q^{81} + 36 q^{82} + 18 q^{86} + 106 q^{88} - 40 q^{92} - 36 q^{94} - 30 q^{96} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1176, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1176, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)