Properties

Label 1110.4.l
Level $1110$
Weight $4$
Character orbit 1110.l
Rep. character $\chi_{1110}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $228$
Sturm bound $912$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1110.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
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 228 1156
Cusp forms 1352 228 1124
Eisenstein series 32 0 32

Trace form

\( 228 q - 912 q^{4} + 24 q^{5} + O(q^{10}) \) \( 228 q - 912 q^{4} + 24 q^{5} - 104 q^{10} + 16 q^{14} + 3648 q^{16} - 136 q^{17} - 72 q^{18} - 424 q^{19} - 96 q^{20} - 288 q^{22} + 156 q^{25} + 608 q^{26} - 708 q^{29} + 152 q^{31} - 320 q^{35} - 608 q^{37} + 696 q^{39} + 416 q^{40} + 180 q^{45} + 1888 q^{50} - 672 q^{51} - 1164 q^{53} - 2896 q^{55} - 64 q^{56} + 792 q^{58} + 104 q^{59} + 124 q^{61} - 64 q^{62} - 14592 q^{64} - 768 q^{65} - 624 q^{66} - 1856 q^{67} + 544 q^{68} - 192 q^{69} - 2016 q^{70} - 2144 q^{71} + 288 q^{72} - 148 q^{73} + 2440 q^{74} + 192 q^{75} + 1696 q^{76} - 5312 q^{77} - 1288 q^{79} + 384 q^{80} - 18468 q^{81} - 704 q^{82} - 2624 q^{86} + 1152 q^{88} - 5364 q^{89} + 2656 q^{91} - 256 q^{94} - 3552 q^{95} - 2960 q^{97} - 8584 q^{98} + O(q^{100}) \)

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

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