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Properties

Label 1150.4.m
Level $1150$
Weight $4$
Character orbit 1150.m
Rep. character $\chi_{1150}(137,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1440$
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.m (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 575 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 4352 1440 2912
Cusp forms 4288 1440 2848
Eisenstein series 64 0 64

Trace form

\( 1440 q + 16 q^{3} + O(q^{10}) \) \( 1440 q + 16 q^{3} + 64 q^{12} - 192 q^{13} + 5760 q^{16} - 32 q^{18} + 604 q^{23} + 2000 q^{25} + 1432 q^{27} - 320 q^{29} + 2752 q^{35} - 12960 q^{36} - 4880 q^{39} + 1576 q^{47} - 256 q^{48} - 272 q^{50} - 768 q^{52} + 1600 q^{55} - 9920 q^{59} + 1376 q^{62} - 6160 q^{69} + 9744 q^{70} - 4960 q^{71} - 128 q^{72} - 10224 q^{73} - 9272 q^{75} - 10128 q^{77} + 6400 q^{78} + 31720 q^{81} + 2800 q^{82} + 904 q^{85} - 2200 q^{87} + 3536 q^{92} - 872 q^{93} - 2944 q^{95} + 448 q^{98} + O(q^{100}) \)

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

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