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Properties

Label 1150.4.i
Level $1150$
Weight $4$
Character orbit 1150.i
Rep. character $\chi_{1150}(139,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $656$
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.i (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 2176 656 1520
Cusp forms 2144 656 1488
Eisenstein series 32 0 32

Trace form

\( 656 q + 656 q^{4} + 12 q^{5} + 24 q^{6} + 1440 q^{9} + O(q^{10}) \) \( 656 q + 656 q^{4} + 12 q^{5} + 24 q^{6} + 1440 q^{9} + 80 q^{10} - 84 q^{15} - 2624 q^{16} + 192 q^{20} - 96 q^{21} + 384 q^{24} - 100 q^{25} - 1616 q^{26} + 1320 q^{27} + 240 q^{28} - 76 q^{29} + 144 q^{30} + 828 q^{31} - 3200 q^{33} - 960 q^{34} + 676 q^{35} - 5760 q^{36} - 1360 q^{37} - 560 q^{39} - 320 q^{40} + 192 q^{41} + 2040 q^{42} + 2180 q^{45} + 184 q^{46} - 2940 q^{47} - 30168 q^{49} + 200 q^{50} - 136 q^{51} + 2380 q^{53} + 240 q^{54} - 1076 q^{55} - 1524 q^{59} + 2016 q^{60} - 1288 q^{61} - 4920 q^{62} - 5800 q^{63} + 10496 q^{64} - 3256 q^{65} - 1088 q^{66} + 1440 q^{67} - 552 q^{69} + 888 q^{70} + 7364 q^{71} - 2280 q^{73} - 752 q^{74} + 5456 q^{75} + 3200 q^{77} + 7080 q^{78} + 672 q^{79} + 192 q^{80} - 10196 q^{81} - 4920 q^{83} - 576 q^{84} - 2796 q^{85} - 8200 q^{87} + 3360 q^{88} - 7224 q^{89} - 9224 q^{90} - 3216 q^{91} - 1408 q^{94} + 3880 q^{95} + 384 q^{96} + 1860 q^{97} - 6560 q^{98} - 4736 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1150, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 2}\)