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Properties

Label 1176.4.ba
Level $1176$
Weight $4$
Character orbit 1176.ba
Rep. character $\chi_{1176}(509,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $944$
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
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 976 400
Cusp forms 1312 944 368
Eisenstein series 64 32 32

Trace form

\( 944 q + 2 q^{4} + 2 q^{9} + O(q^{10}) \) \( 944 q + 2 q^{4} + 2 q^{9} + 6 q^{10} - 162 q^{12} + 92 q^{15} - 238 q^{16} - 66 q^{18} + 300 q^{22} + 84 q^{24} + 11004 q^{25} + 556 q^{30} + 12 q^{31} + 6 q^{33} + 124 q^{36} + 56 q^{39} - 414 q^{40} + 1348 q^{46} + 1632 q^{52} + 480 q^{54} - 124 q^{57} - 894 q^{58} + 1248 q^{60} - 1636 q^{64} - 2376 q^{66} - 1002 q^{72} + 660 q^{73} + 196 q^{78} - 956 q^{79} + 618 q^{81} + 360 q^{82} + 168 q^{87} + 5790 q^{88} - 4476 q^{94} + 1782 q^{96} + O(q^{100}) \)

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

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