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Properties

Label 1150.4.s
Level $1150$
Weight $4$
Character orbit 1150.s
Rep. character $\chi_{1150}(31,\cdot)$
Character field $\Q(\zeta_{55})$
Dimension $7200$
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.s (of order \(55\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 575 \)
Character field: \(\Q(\zeta_{55})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 21760 7200 14560
Cusp forms 21440 7200 14240
Eisenstein series 320 0 320

Trace form

\( 7200 q - 16 q^{3} + 720 q^{4} - 80 q^{5} + 16 q^{7} + 1748 q^{9} + O(q^{10}) \) \( 7200 q - 16 q^{3} + 720 q^{4} - 80 q^{5} + 16 q^{7} + 1748 q^{9} - 212 q^{11} + 96 q^{12} - 192 q^{13} - 112 q^{14} - 304 q^{15} + 2880 q^{16} - 384 q^{17} + 144 q^{18} - 220 q^{19} + 352 q^{20} - 168 q^{21} + 432 q^{22} - 2262 q^{23} + 1112 q^{25} + 944 q^{27} - 288 q^{28} + 96 q^{29} - 1416 q^{30} - 144 q^{31} - 4320 q^{33} - 272 q^{34} - 1396 q^{35} + 6992 q^{36} - 1656 q^{37} - 352 q^{38} - 1464 q^{39} + 624 q^{43} + 272 q^{44} + 44 q^{45} - 648 q^{46} - 3408 q^{47} + 384 q^{48} - 36240 q^{49} + 728 q^{50} + 1632 q^{51} - 768 q^{52} - 1768 q^{53} - 3084 q^{55} - 448 q^{56} - 7112 q^{57} - 2976 q^{59} - 2792 q^{60} + 580 q^{61} + 2104 q^{62} - 7744 q^{63} + 11520 q^{64} + 7068 q^{65} - 1056 q^{66} - 5736 q^{67} + 1024 q^{68} - 17180 q^{69} + 9928 q^{70} + 10812 q^{71} - 128 q^{72} + 6744 q^{73} + 5920 q^{74} - 13870 q^{75} + 1600 q^{76} + 4064 q^{77} + 5896 q^{78} + 4928 q^{79} - 1408 q^{80} + 8376 q^{81} + 2800 q^{82} - 1980 q^{83} - 672 q^{84} - 15222 q^{85} - 1384 q^{86} - 1348 q^{87} - 1152 q^{88} - 2456 q^{89} + 6256 q^{90} + 12320 q^{91} - 2832 q^{92} - 6616 q^{93} + 96 q^{94} - 22668 q^{95} - 18744 q^{97} - 14352 q^{98} - 17008 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1150, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 2}\)