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Properties

Label 1150.4.r
Level $1150$
Weight $4$
Character orbit 1150.r
Rep. character $\chi_{1150}(7,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $2160$
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.r (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 11040 2160 8880
Cusp forms 10560 2160 8400
Eisenstein series 480 0 480

Trace form

\( 2160 q - 16 q^{3} - 32 q^{6} + O(q^{10}) \) \( 2160 q - 16 q^{3} - 32 q^{6} - 64 q^{12} + 192 q^{13} + 3456 q^{16} - 144 q^{18} - 1660 q^{23} + 608 q^{26} + 728 q^{27} + 352 q^{28} + 1216 q^{31} + 3872 q^{33} - 7328 q^{36} + 2376 q^{37} - 4416 q^{41} - 512 q^{46} - 3640 q^{47} + 256 q^{48} + 768 q^{52} + 7744 q^{56} + 7656 q^{57} - 4224 q^{61} - 1376 q^{62} - 21824 q^{66} + 21456 q^{71} + 128 q^{72} - 1296 q^{73} - 752 q^{77} + 6000 q^{78} + 44696 q^{81} + 80 q^{82} + 20944 q^{86} + 6760 q^{87} + 1104 q^{92} - 5288 q^{93} + 512 q^{96} - 25344 q^{97} - 14352 q^{98} + O(q^{100}) \)

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

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