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Properties

Label 1110.4.k
Level $1110$
Weight $4$
Character orbit 1110.k
Rep. character $\chi_{1110}(179,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $456$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 555 \)
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 456 928
Cusp forms 1352 456 896
Eisenstein series 32 0 32

Trace form

\( 456 q - 256 q^{9} + O(q^{10}) \) \( 456 q - 256 q^{9} + 140 q^{15} - 7296 q^{16} - 288 q^{19} - 216 q^{31} + 288 q^{34} + 608 q^{39} + 1124 q^{45} + 1728 q^{46} - 20040 q^{49} + 1144 q^{51} + 720 q^{55} - 560 q^{60} + 2448 q^{61} + 96 q^{66} + 2456 q^{69} - 2016 q^{70} + 6220 q^{75} - 1152 q^{76} - 1272 q^{79} - 2016 q^{81} - 2440 q^{90} + 432 q^{91} - 3792 q^{94} + O(q^{100}) \)

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

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