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Properties

Label 1911.4.bh
Level $1911$
Weight $4$
Character orbit 1911.bh
Rep. character $\chi_{1911}(521,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $960$
Sturm bound $1045$

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Defining parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1911.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1045\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1911, [\chi])\).

Total New Old
Modular forms 1600 960 640
Cusp forms 1536 960 576
Eisenstein series 64 0 64

Trace form

\( 960 q + 1920 q^{4} + 28 q^{9} + O(q^{10}) \) \( 960 q + 1920 q^{4} + 28 q^{9} + 72 q^{10} - 330 q^{12} + 168 q^{15} - 7200 q^{16} + 70 q^{18} + 432 q^{22} + 288 q^{24} - 12108 q^{25} - 1524 q^{30} - 828 q^{31} + 2252 q^{36} + 600 q^{37} + 864 q^{40} - 1344 q^{43} + 4740 q^{45} + 2256 q^{46} - 2214 q^{51} - 7902 q^{54} + 3712 q^{57} + 6072 q^{58} - 2076 q^{60} + 216 q^{61} - 56784 q^{64} + 3282 q^{66} + 3264 q^{67} - 5518 q^{72} - 2304 q^{73} - 984 q^{75} + 1820 q^{78} - 204 q^{79} + 1068 q^{81} + 5832 q^{82} + 10560 q^{85} + 2496 q^{87} - 2712 q^{88} - 4832 q^{93} - 1944 q^{94} - 13134 q^{96} + 16712 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1911, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1911, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)