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Properties

Label 1150.2.r
Level $1150$
Weight $2$
Character orbit 1150.r
Rep. character $\chi_{1150}(7,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $720$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1150.r (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1150, [\chi])\).

Total New Old
Modular forms 3840 720 3120
Cusp forms 3360 720 2640
Eisenstein series 480 0 480

Trace form

\( 720 q + 8 q^{3} + 16 q^{6} + O(q^{10}) \) \( 720 q + 8 q^{3} + 16 q^{6} + 8 q^{12} - 16 q^{13} + 72 q^{16} + 72 q^{18} + 80 q^{23} + 16 q^{26} - 16 q^{27} + 44 q^{28} - 48 q^{31} + 44 q^{33} - 56 q^{36} + 88 q^{37} + 48 q^{41} + 16 q^{46} + 80 q^{47} - 8 q^{48} - 16 q^{52} + 88 q^{56} + 88 q^{57} + 352 q^{61} + 32 q^{62} + 352 q^{66} - 408 q^{71} - 16 q^{72} + 88 q^{73} + 24 q^{77} - 40 q^{78} + 152 q^{81} - 40 q^{82} + 88 q^{86} - 40 q^{87} - 8 q^{92} - 56 q^{93} - 16 q^{96} - 132 q^{97} - 24 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1150, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1150, [\chi])\) into lower level spaces

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