Properties

Label 1176.4.bo
Level $1176$
Weight $4$
Character orbit 1176.bo
Rep. character $\chi_{1176}(125,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $4008$
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.bo (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1176 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 4056 4056 0
Cusp forms 4008 4008 0
Eisenstein series 48 48 0

Trace form

\( 4008 q - 10 q^{4} - 7 q^{6} - 24 q^{7} - 10 q^{9} + O(q^{10}) \) \( 4008 q - 10 q^{4} - 7 q^{6} - 24 q^{7} - 10 q^{9} - 14 q^{10} - 392 q^{12} - 118 q^{15} - 10 q^{16} - 98 q^{18} - 230 q^{22} - 7 q^{24} + 16280 q^{25} - 208 q^{28} - 224 q^{30} - 14 q^{33} + 490 q^{34} - 577 q^{36} + 98 q^{39} - 518 q^{40} - 355 q^{42} + 378 q^{46} + 336 q^{49} - 14 q^{52} - 7 q^{54} - 28 q^{55} - 280 q^{57} - 986 q^{58} - 2631 q^{60} + 694 q^{63} - 262 q^{64} - 2191 q^{66} + 2452 q^{70} - 2107 q^{72} - 28 q^{73} - 9478 q^{76} + 7833 q^{78} - 48 q^{79} - 3090 q^{81} - 6104 q^{82} + 4054 q^{84} - 14 q^{87} + 3550 q^{88} + 4571 q^{90} - 3794 q^{94} - 5390 q^{96} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1176, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.