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Properties

Label 1176.4.t
Level $1176$
Weight $4$
Character orbit 1176.t
Rep. character $\chi_{1176}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $480$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1176.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1176, [\chi])\).

Total New Old
Modular forms 1376 480 896
Cusp forms 1312 480 832
Eisenstein series 64 0 64

Trace form

\( 480 q - 4 q^{2} + 20 q^{4} - 52 q^{8} + 2160 q^{9} + O(q^{10}) \) \( 480 q - 4 q^{2} + 20 q^{4} - 52 q^{8} + 2160 q^{9} - 18 q^{10} - 80 q^{11} - 4 q^{16} + 36 q^{18} + 244 q^{22} - 270 q^{24} - 6000 q^{25} - 750 q^{26} - 168 q^{30} + 286 q^{32} + 360 q^{36} + 1494 q^{38} - 1170 q^{40} + 3232 q^{43} + 88 q^{44} - 1476 q^{46} + 1736 q^{50} + 3564 q^{52} + 336 q^{57} - 402 q^{58} - 4128 q^{59} - 1434 q^{60} + 3104 q^{64} - 2052 q^{66} + 1032 q^{67} + 1392 q^{68} - 234 q^{72} + 648 q^{73} - 622 q^{74} - 1620 q^{78} + 1548 q^{80} - 19440 q^{81} - 4596 q^{82} - 5610 q^{86} - 5030 q^{88} + 4312 q^{92} + 2052 q^{94} - 3870 q^{96} - 1440 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1176, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

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