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Properties

Label 1334.2.h
Level $1334$
Weight $2$
Character orbit 1334.h
Rep. character $\chi_{1334}(59,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $560$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 1334 = 2 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1334.h (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 \(M_{2}(1334, [\chi])\).

Total New Old
Modular forms 1840 560 1280
Cusp forms 1760 560 1200
Eisenstein series 80 0 80

Trace form

\( 560 q + 8 q^{3} - 56 q^{4} + 16 q^{5} + 8 q^{7} - 48 q^{9} + O(q^{10}) \) \( 560 q + 8 q^{3} - 56 q^{4} + 16 q^{5} + 8 q^{7} - 48 q^{9} + 4 q^{10} + 28 q^{11} + 8 q^{12} + 8 q^{13} + 16 q^{14} - 12 q^{15} - 56 q^{16} - 20 q^{17} - 56 q^{18} + 12 q^{19} - 28 q^{20} + 24 q^{21} + 16 q^{22} + 20 q^{23} - 8 q^{25} + 24 q^{26} + 32 q^{27} - 36 q^{28} - 56 q^{30} - 12 q^{31} - 20 q^{33} - 20 q^{35} - 48 q^{36} - 44 q^{37} + 8 q^{38} + 48 q^{39} + 4 q^{40} + 12 q^{41} + 16 q^{42} + 44 q^{43} + 28 q^{44} + 112 q^{45} + 16 q^{46} - 56 q^{47} + 8 q^{48} + 24 q^{49} + 24 q^{50} + 80 q^{51} + 8 q^{52} + 12 q^{53} + 112 q^{55} + 16 q^{56} - 40 q^{57} - 148 q^{59} - 12 q^{60} - 108 q^{61} + 40 q^{62} + 128 q^{63} - 56 q^{64} - 188 q^{65} + 32 q^{66} + 64 q^{67} - 64 q^{68} - 128 q^{69} - 88 q^{70} - 140 q^{71} - 56 q^{72} + 64 q^{73} + 8 q^{74} - 208 q^{75} + 12 q^{76} + 56 q^{77} + 32 q^{78} - 164 q^{79} - 28 q^{80} - 176 q^{81} + 40 q^{82} + 72 q^{83} + 24 q^{84} + 52 q^{85} + 32 q^{86} + 16 q^{88} + 88 q^{89} + 68 q^{90} + 112 q^{91} + 20 q^{92} + 168 q^{93} + 56 q^{94} + 44 q^{95} - 12 q^{97} + 80 q^{98} - 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1334, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1334, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1334, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(667, [\chi])\)\(^{\oplus 2}\)