Properties

Label 1339.2.q
Level $1339$
Weight $2$
Character orbit 1339.q
Rep. character $\chi_{1339}(413,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $236$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(242\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1339, [\chi])\).

Total New Old
Modular forms 248 236 12
Cusp forms 240 236 4
Eisenstein series 8 0 8

Trace form

\( 236 q + 116 q^{4} - 18 q^{6} - 114 q^{9} + O(q^{10}) \) \( 236 q + 116 q^{4} - 18 q^{6} - 114 q^{9} + 4 q^{10} + 12 q^{12} - 2 q^{13} - 24 q^{14} - 120 q^{16} - 10 q^{17} + 12 q^{20} + 6 q^{22} - 16 q^{23} - 36 q^{24} - 240 q^{25} + 4 q^{26} + 36 q^{27} + 15 q^{28} + 66 q^{32} + 6 q^{33} - 12 q^{35} + 110 q^{36} - 42 q^{37} - 18 q^{38} - 10 q^{39} + 4 q^{40} + 12 q^{41} - 28 q^{42} + 4 q^{43} + 30 q^{45} + 69 q^{46} + 24 q^{48} + 122 q^{49} - 30 q^{50} - 36 q^{51} + 40 q^{52} + 48 q^{53} + 54 q^{54} + 6 q^{55} - 49 q^{56} - 60 q^{58} - 72 q^{59} + 6 q^{61} + 26 q^{62} - 6 q^{63} - 252 q^{64} + 34 q^{65} - 64 q^{66} + 22 q^{68} - 36 q^{69} + 12 q^{71} - 54 q^{72} + 8 q^{74} + 2 q^{75} + 30 q^{76} - 64 q^{77} - 14 q^{78} - 24 q^{79} + 138 q^{80} - 134 q^{81} - 39 q^{82} - 24 q^{84} - 42 q^{85} + 6 q^{87} - 4 q^{88} - 18 q^{89} - 52 q^{90} - 2 q^{91} + 78 q^{93} + 6 q^{94} + 64 q^{95} - 27 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1339, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1339, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1339, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)