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Properties

Label 2601.2.e
Level $2601$
Weight $2$
Character orbit 2601.e
Rep. character $\chi_{2601}(868,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $512$
Sturm bound $612$

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Defining parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(612\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2601, [\chi])\).

Total New Old
Modular forms 648 572 76
Cusp forms 576 512 64
Eisenstein series 72 60 12

Trace form

\( 512 q + 2 q^{3} - 240 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 12 q^{8} + 6 q^{9} + O(q^{10}) \) \( 512 q + 2 q^{3} - 240 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 12 q^{8} + 6 q^{9} + 8 q^{11} - 4 q^{12} + 2 q^{13} + 4 q^{14} - 12 q^{15} - 208 q^{16} - 46 q^{18} - 4 q^{19} - 10 q^{20} + 16 q^{21} + 8 q^{23} + 18 q^{24} - 198 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{28} - 6 q^{29} + 6 q^{30} + 2 q^{31} - 12 q^{32} + 24 q^{33} - 44 q^{35} - 58 q^{36} + 8 q^{37} - 36 q^{38} + 6 q^{39} + 12 q^{41} + 10 q^{42} + 8 q^{43} - 60 q^{44} + 24 q^{46} + 4 q^{47} - 50 q^{48} - 170 q^{49} - 24 q^{50} - 26 q^{52} - 38 q^{54} - 12 q^{55} + 24 q^{56} + 56 q^{57} - 6 q^{58} - 24 q^{59} + 142 q^{60} + 2 q^{61} - 108 q^{62} + 44 q^{63} + 324 q^{64} - 20 q^{65} + 16 q^{66} + 8 q^{67} + 4 q^{69} - 4 q^{71} + 46 q^{72} - 28 q^{73} + 46 q^{74} - 50 q^{75} + 8 q^{76} - 12 q^{77} + 96 q^{78} + 14 q^{79} + 148 q^{80} - 26 q^{81} + 36 q^{82} - 26 q^{83} - 36 q^{84} - 44 q^{86} - 22 q^{87} + 24 q^{88} + 56 q^{89} - 10 q^{90} - 44 q^{91} - 4 q^{92} - 6 q^{93} - 6 q^{94} + 64 q^{95} - 6 q^{96} - 4 q^{97} - 76 q^{98} + 26 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2601, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2601, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2601, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 2}\)