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Properties

Label 1176.4.cc
Level $1176$
Weight $4$
Character orbit 1176.cc
Rep. character $\chi_{1176}(5,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $8016$
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.cc (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1176 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 8112 8112 0
Cusp forms 8016 8016 0
Eisenstein series 96 96 0

Trace form

\( 8016 q - 26 q^{4} - 14 q^{6} - 48 q^{7} - 26 q^{9} + O(q^{10}) \) \( 8016 q - 26 q^{4} - 14 q^{6} - 48 q^{7} - 26 q^{9} - 22 q^{10} + 209 q^{12} + 88 q^{15} - 26 q^{16} - 25 q^{18} + 200 q^{22} + 70 q^{24} - 16352 q^{25} - 476 q^{28} - 193 q^{30} - 72 q^{31} - 22 q^{33} - 532 q^{34} + 562 q^{36} + 28 q^{39} + 62 q^{40} + 1042 q^{42} + 216 q^{46} - 408 q^{49} + 1604 q^{52} + 466 q^{54} - 56 q^{55} + 250 q^{57} - 514 q^{58} + 4194 q^{60} - 670 q^{63} + 232 q^{64} - 206 q^{66} + 104 q^{70} - 1064 q^{72} + 604 q^{73} + 9436 q^{76} - 6552 q^{78} - 24 q^{79} + 4902 q^{81} + 6422 q^{82} + 17240 q^{84} + 140 q^{87} + 1754 q^{88} + 11767 q^{90} - 724 q^{94} - 26764 q^{96} + O(q^{100}) \)

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.