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Properties

Label 1176.4.i
Level $1176$
Weight $4$
Character orbit 1176.i
Rep. character $\chi_{1176}(293,\cdot)$
Character field $\Q$
Dimension $472$
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.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
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 688 488 200
Cusp forms 656 472 184
Eisenstein series 32 16 16

Trace form

\( 472 q + 4 q^{4} + 4 q^{9} + O(q^{10}) \) \( 472 q + 4 q^{4} + 4 q^{9} - 116 q^{15} + 244 q^{16} - 36 q^{18} - 180 q^{22} - 10992 q^{25} - 952 q^{30} - 796 q^{36} + 112 q^{39} - 712 q^{46} + 100 q^{57} - 564 q^{58} + 336 q^{60} - 1196 q^{64} - 2148 q^{72} + 1652 q^{78} + 968 q^{79} + 1236 q^{81} - 444 q^{88} + O(q^{100}) \)

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

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