Properties

Label 1150.2.k
Level $1150$
Weight $2$
Character orbit 1150.k
Rep. character $\chi_{1150}(101,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $380$
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.k (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(360\)

Dimensions

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

Total New Old
Modular forms 1920 380 1540
Cusp forms 1680 380 1300
Eisenstein series 240 0 240

Trace form

\( 380 q + 4 q^{3} - 38 q^{4} + 4 q^{6} + 4 q^{7} - 30 q^{9} + O(q^{10}) \) \( 380 q + 4 q^{3} - 38 q^{4} + 4 q^{6} + 4 q^{7} - 30 q^{9} + 6 q^{11} + 4 q^{12} + 4 q^{13} + 12 q^{14} - 38 q^{16} + 14 q^{17} - 44 q^{18} + 32 q^{19} + 58 q^{21} + 28 q^{22} - 44 q^{23} + 4 q^{24} + 14 q^{26} + 58 q^{27} - 18 q^{28} + 22 q^{29} + 38 q^{31} - 46 q^{33} + 4 q^{34} - 30 q^{36} - 38 q^{37} - 6 q^{38} - 36 q^{39} + 30 q^{41} - 32 q^{42} + 78 q^{43} + 6 q^{44} + 10 q^{46} - 68 q^{47} + 4 q^{48} - 56 q^{49} + 44 q^{51} + 4 q^{52} - 4 q^{53} - 30 q^{54} - 10 q^{56} - 26 q^{57} + 16 q^{58} - 94 q^{59} - 50 q^{61} + 66 q^{62} + 106 q^{63} - 38 q^{64} - 72 q^{66} + 58 q^{67} + 36 q^{68} + 314 q^{69} + 250 q^{71} + 44 q^{72} + 52 q^{73} - 70 q^{74} + 10 q^{76} + 94 q^{77} + 82 q^{78} - 22 q^{79} - 170 q^{81} + 48 q^{82} + 110 q^{83} - 30 q^{84} - 4 q^{86} + 82 q^{87} + 6 q^{88} - 14 q^{89} + 36 q^{91} + 40 q^{93} + 48 q^{94} + 4 q^{96} - 28 q^{97} - 28 q^{98} - 102 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 2}\)