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Properties

Label 1176.2.i
Level $1176$
Weight $2$
Character orbit 1176.i
Rep. character $\chi_{1176}(293,\cdot)$
Character field $\Q$
Dimension $152$
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.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 240 168 72
Cusp forms 208 152 56
Eisenstein series 32 16 16

Trace form

\( 152 q + 4 q^{4} + 4 q^{9} + O(q^{10}) \) \( 152 q + 4 q^{4} + 4 q^{9} - 20 q^{15} - 12 q^{16} + 28 q^{22} - 112 q^{25} - 4 q^{30} + 44 q^{36} + 16 q^{39} - 16 q^{46} + 4 q^{57} + 36 q^{58} - 24 q^{60} + 52 q^{64} + 12 q^{72} - 124 q^{78} - 56 q^{79} - 12 q^{81} - 28 q^{88} + O(q^{100}) \)

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

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