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Properties

Label 1110.4.ch
Level $1110$
Weight $4$
Character orbit 1110.ch
Rep. character $\chi_{1110}(13,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1368$
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.ch (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(912\)

Dimensions

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

Total New Old
Modular forms 8304 1368 6936
Cusp forms 8112 1368 6744
Eisenstein series 192 0 192

Trace form

\( 1368 q + O(q^{10}) \) \( 1368 q + 96 q^{14} + 204 q^{17} + 288 q^{20} - 300 q^{25} + 288 q^{30} + 408 q^{31} - 6384 q^{35} + 648 q^{37} + 144 q^{39} + 960 q^{40} + 1380 q^{41} - 672 q^{44} + 768 q^{49} + 6720 q^{50} + 3744 q^{53} - 6696 q^{57} - 360 q^{58} + 9384 q^{61} + 96 q^{62} + 43776 q^{64} + 1152 q^{65} - 864 q^{67} + 3024 q^{70} - 6432 q^{71} + 444 q^{73} - 7320 q^{74} - 1632 q^{76} + 6624 q^{77} - 3024 q^{79} + 10896 q^{83} + 3936 q^{86} + 1728 q^{88} + 6072 q^{89} + 12480 q^{91} - 1368 q^{93} - 11616 q^{95} + 16128 q^{97} + 7584 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)