↑

Properties

Label 1334.2.u
Level $1334$
Weight $2$
Character orbit 1334.u
Rep. character $\chi_{1334}(9,\cdot)$
Character field $\Q(\zeta_{154})$
Dimension $3600$
Sturm bound $360$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1334 = 2 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1334.u (of order \(154\) and degree \(60\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{154})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1334, [\chi])\).

Total New Old
Modular forms 11040 3600 7440
Cusp forms 10560 3600 6960
Eisenstein series 480 0 480

Trace form

\( 3600 q - 60 q^{4} + 4 q^{5} + 20 q^{6} - 68 q^{9} + O(q^{10}) \) \( 3600 q - 60 q^{4} + 4 q^{5} + 20 q^{6} - 68 q^{9} + 40 q^{13} + 60 q^{16} - 4 q^{20} + 28 q^{21} - 40 q^{22} + 104 q^{23} - 20 q^{24} + 224 q^{25} - 84 q^{27} - 42 q^{29} + 40 q^{30} - 28 q^{31} + 24 q^{33} + 8 q^{34} - 8 q^{35} + 40 q^{36} - 28 q^{37} - 12 q^{38} + 16 q^{42} + 56 q^{43} + 112 q^{45} - 28 q^{47} - 242 q^{49} + 56 q^{50} + 148 q^{51} + 16 q^{52} - 12 q^{53} + 24 q^{54} - 252 q^{55} + 4 q^{57} + 44 q^{58} + 24 q^{59} - 56 q^{61} + 108 q^{62} + 248 q^{63} - 60 q^{64} - 124 q^{67} + 28 q^{69} + 40 q^{71} - 440 q^{74} - 56 q^{76} + 630 q^{77} - 24 q^{78} - 56 q^{79} + 4 q^{80} - 4 q^{81} - 164 q^{82} - 52 q^{83} - 84 q^{84} - 56 q^{85} - 164 q^{86} - 58 q^{87} + 24 q^{88} + 112 q^{89} - 140 q^{90} - 160 q^{91} - 16 q^{92} + 56 q^{93} + 76 q^{94} - 112 q^{95} - 8 q^{96} - 56 q^{97} + O(q^{100}) \)

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

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