↑

Properties

Label 1176.4.ch
Level $1176$
Weight $4$
Character orbit 1176.ch
Rep. character $\chi_{1176}(11,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $8016$
Sturm bound $896$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1176.ch (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

\( 8016 q - 26 q^{3} - 26 q^{4} + 6 q^{6} - 26 q^{9} + O(q^{10}) \) \( 8016 q - 26 q^{3} - 26 q^{4} + 6 q^{6} - 26 q^{9} - 58 q^{10} + 373 q^{12} - 26 q^{16} + 45 q^{18} - 24 q^{19} + 264 q^{22} + 210 q^{24} + 16248 q^{25} - 20 q^{27} - 436 q^{28} + 73 q^{30} + 82 q^{33} + 732 q^{34} - 838 q^{36} + 974 q^{40} - 762 q^{42} - 40 q^{43} - 268 q^{46} + 388 q^{48} - 408 q^{49} - 618 q^{51} - 628 q^{52} + 1406 q^{54} + 250 q^{57} + 494 q^{58} + 3566 q^{60} - 2792 q^{64} - 3396 q^{66} - 24 q^{67} - 6988 q^{70} - 1064 q^{72} - 268 q^{73} + 116 q^{75} - 4204 q^{76} + 788 q^{78} - 4954 q^{81} + 9474 q^{82} - 10528 q^{84} - 294 q^{88} - 6309 q^{90} - 13592 q^{91} + 1148 q^{94} + 24244 q^{96} + 4560 q^{97} + 2868 q^{99} + O(q^{100}) \)

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.