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Properties

Label 1176.2.bn
Level $1176$
Weight $2$
Character orbit 1176.bn
Rep. character $\chi_{1176}(155,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1320$
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.bn (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1176 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 1368 1368 0
Cusp forms 1320 1320 0
Eisenstein series 48 48 0

Trace form

\( 1320 q - 10 q^{3} - 10 q^{4} - 9 q^{6} - 10 q^{9} + O(q^{10}) \) \( 1320 q - 10 q^{3} - 10 q^{4} - 9 q^{6} - 10 q^{9} - 2 q^{10} + 26 q^{12} - 10 q^{16} - 6 q^{18} - 48 q^{19} - 6 q^{22} - 21 q^{24} - 224 q^{25} - 10 q^{27} - 48 q^{28} + 8 q^{30} - 22 q^{33} + 34 q^{34} - 17 q^{36} - 50 q^{40} + 3 q^{42} - 20 q^{43} + 18 q^{46} - 4 q^{48} - 32 q^{49} + 18 q^{51} - 58 q^{52} - 5 q^{54} - 40 q^{57} + 14 q^{58} + 61 q^{60} - 22 q^{64} + 105 q^{66} - 48 q^{67} + 68 q^{70} - 43 q^{72} - 36 q^{73} + 22 q^{75} - 194 q^{76} - 107 q^{78} - 50 q^{81} - 44 q^{82} - 98 q^{84} - 66 q^{88} + 123 q^{90} - 196 q^{91} + 22 q^{94} - 34 q^{96} - 16 q^{97} - 60 q^{99} + O(q^{100}) \)

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.