Properties

Label 1014.2.q
Level $1014$
Weight $2$
Character orbit 1014.q
Rep. character $\chi_{1014}(55,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $720$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.q (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1014, [\chi])\).

Total New Old
Modular forms 4464 720 3744
Cusp forms 4272 720 3552
Eisenstein series 192 0 192

Trace form

\( 720q - 2q^{2} + 30q^{4} - 4q^{5} + 4q^{8} + 30q^{9} + O(q^{10}) \) \( 720q - 2q^{2} + 30q^{4} - 4q^{5} + 4q^{8} + 30q^{9} - 2q^{10} + 8q^{11} + 2q^{13} - 8q^{14} + 4q^{15} + 30q^{16} + 6q^{17} + 4q^{18} + 2q^{20} - 8q^{21} + 48q^{22} + 8q^{23} - 72q^{25} - 2q^{26} + 6q^{29} - 4q^{30} + 68q^{31} - 2q^{32} + 4q^{33} + 4q^{34} + 16q^{35} + 30q^{36} - 18q^{37} - 8q^{38} - 12q^{39} + 30q^{40} + 2q^{41} - 4q^{42} + 8q^{43} - 16q^{44} + 2q^{45} - 16q^{47} + 86q^{49} - 4q^{52} + 102q^{53} + 128q^{55} + 4q^{56} - 8q^{57} + 58q^{58} - 8q^{59} + 44q^{60} - 6q^{61} + 12q^{62} - 60q^{64} + 26q^{65} + 8q^{66} + 148q^{67} + 6q^{68} - 4q^{69} + 224q^{70} - 320q^{71} - 2q^{72} + 52q^{73} + 200q^{74} + 8q^{75} + 52q^{76} - 32q^{77} - 24q^{79} + 2q^{80} + 30q^{81} + 2q^{82} + 4q^{84} + 116q^{85} + 156q^{86} + 68q^{87} - 4q^{88} + 20q^{89} + 4q^{90} + 104q^{91} - 16q^{92} + 156q^{93} + 52q^{94} - 392q^{95} + 168q^{97} + 6q^{98} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1014, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1014, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)