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Properties

Label 1150.4.k
Level $1150$
Weight $4$
Character orbit 1150.k
Rep. character $\chi_{1150}(101,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $1140$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1150.k (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1150, [\chi])\).

Total New Old
Modular forms 5520 1140 4380
Cusp forms 5280 1140 4140
Eisenstein series 240 0 240

Trace form

\( 1140 q - 8 q^{3} - 456 q^{4} - 8 q^{6} + 8 q^{7} - 934 q^{9} + O(q^{10}) \) \( 1140 q - 8 q^{3} - 456 q^{4} - 8 q^{6} + 8 q^{7} - 934 q^{9} + 46 q^{11} - 32 q^{12} - 80 q^{13} + 40 q^{14} - 1824 q^{16} + 404 q^{17} + 184 q^{18} - 102 q^{19} - 1020 q^{21} - 584 q^{22} + 1100 q^{23} - 32 q^{24} - 108 q^{26} + 136 q^{27} - 144 q^{28} + 484 q^{29} + 504 q^{31} - 1412 q^{33} - 40 q^{34} - 3736 q^{36} - 762 q^{37} + 84 q^{38} + 288 q^{39} - 1466 q^{41} + 64 q^{42} - 1286 q^{43} + 184 q^{44} + 372 q^{46} + 1936 q^{47} - 128 q^{48} - 5096 q^{49} - 1488 q^{51} - 320 q^{52} + 504 q^{53} - 2292 q^{54} - 1776 q^{56} + 2252 q^{57} + 1552 q^{58} - 2734 q^{59} + 1134 q^{61} - 2244 q^{62} - 5224 q^{63} - 7296 q^{64} + 3760 q^{66} - 2946 q^{67} - 2080 q^{68} - 19784 q^{69} - 16008 q^{71} - 2080 q^{72} - 2428 q^{73} + 1884 q^{74} + 472 q^{76} - 1152 q^{77} + 508 q^{78} - 358 q^{79} - 15366 q^{81} + 3920 q^{82} + 8008 q^{83} - 2584 q^{84} - 6096 q^{86} - 9458 q^{87} - 400 q^{88} - 4514 q^{89} + 608 q^{91} + 528 q^{92} - 4260 q^{93} + 1008 q^{94} - 128 q^{96} - 12266 q^{97} - 8232 q^{98} - 18264 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1150, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1150, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1150, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 2}\)