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Properties

Label 1110.4.m
Level $1110$
Weight $4$
Character orbit 1110.m
Rep. character $\chi_{1110}(593,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $432$
Sturm bound $912$

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Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1110.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(912\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1110, [\chi])\).

Total New Old
Modular forms 1384 432 952
Cusp forms 1352 432 920
Eisenstein series 32 0 32

Trace form

\( 432 q - 16 q^{6} - 24 q^{7} + O(q^{10}) \) \( 432 q - 16 q^{6} - 24 q^{7} - 48 q^{10} + 192 q^{13} + 336 q^{15} - 6912 q^{16} + 32 q^{18} - 928 q^{21} - 336 q^{22} + 528 q^{27} - 96 q^{28} - 872 q^{33} - 736 q^{36} + 3936 q^{43} + 3584 q^{45} + 2016 q^{46} - 576 q^{51} - 768 q^{52} + 1752 q^{55} - 2160 q^{57} - 2352 q^{58} - 704 q^{60} + 144 q^{61} - 2536 q^{63} + 96 q^{66} - 1968 q^{67} + 3216 q^{70} - 128 q^{72} + 2568 q^{73} + 1840 q^{75} + 6920 q^{78} + 2712 q^{81} + 576 q^{82} - 4032 q^{85} - 8128 q^{87} - 1344 q^{88} - 4032 q^{91} + 6040 q^{93} + 256 q^{96} + 1560 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1110, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1110, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)