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Properties

Label 1176.4.j
Level $1176$
Weight $4$
Character orbit 1176.j
Rep. character $\chi_{1176}(491,\cdot)$
Character field $\Q$
Dimension $482$
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.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 688 502 186
Cusp forms 656 482 174
Eisenstein series 32 20 12

Trace form

\( 482 q + 2 q^{3} + 8 q^{4} - 22 q^{6} + 2 q^{9} + O(q^{10}) \) \( 482 q + 2 q^{3} + 8 q^{4} - 22 q^{6} + 2 q^{9} + 12 q^{10} + 122 q^{12} + 92 q^{16} + 288 q^{18} - 20 q^{19} - 20 q^{22} + 26 q^{24} + 11054 q^{25} - 130 q^{27} + 116 q^{30} - 168 q^{33} - 488 q^{34} + 160 q^{36} + 180 q^{40} + 412 q^{43} - 240 q^{46} + 1250 q^{48} - 428 q^{51} + 1092 q^{52} + 342 q^{54} + 216 q^{57} + 1572 q^{58} - 1120 q^{60} + 1316 q^{64} + 1776 q^{66} + 1636 q^{67} - 2748 q^{72} - 212 q^{73} - 1346 q^{75} + 2068 q^{76} + 3356 q^{78} - 1074 q^{81} - 1064 q^{82} - 956 q^{88} + 5048 q^{90} + 2928 q^{94} + 606 q^{96} + 52 q^{97} + 1188 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1176, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)