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Properties

Label 2601.2.s
Level $2601$
Weight $2$
Character orbit 2601.s
Rep. character $\chi_{2601}(688,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $2048$
Sturm bound $612$

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Defining parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.s (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 153 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(612\)

Dimensions

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

Total New Old
Modular forms 2592 2272 320
Cusp forms 2304 2048 256
Eisenstein series 288 224 64

Trace form

\( 2048 q + 4 q^{2} + 8 q^{3} + 4 q^{5} + 8 q^{6} + 4 q^{7} + 32 q^{8} + 20 q^{9} + O(q^{10}) \) \( 2048 q + 4 q^{2} + 8 q^{3} + 4 q^{5} + 8 q^{6} + 4 q^{7} + 32 q^{8} + 20 q^{9} + 16 q^{10} + 44 q^{12} + 4 q^{14} + 4 q^{15} + 864 q^{16} - 144 q^{18} + 16 q^{19} + 36 q^{20} + 4 q^{22} - 8 q^{23} - 28 q^{24} + 4 q^{25} + 32 q^{26} + 32 q^{27} + 48 q^{28} + 4 q^{29} + 4 q^{31} - 28 q^{32} + 48 q^{33} - 352 q^{35} + 44 q^{36} + 16 q^{37} + 28 q^{39} - 12 q^{40} - 20 q^{41} - 48 q^{42} + 16 q^{43} - 16 q^{44} + 4 q^{45} - 32 q^{46} + 24 q^{48} + 4 q^{49} + 112 q^{50} + 8 q^{52} - 16 q^{53} - 88 q^{54} + 76 q^{56} - 64 q^{57} + 4 q^{58} - 56 q^{59} + 8 q^{60} + 4 q^{61} + 16 q^{62} - 84 q^{63} + 52 q^{65} - 176 q^{66} + 8 q^{67} + 80 q^{69} + 12 q^{70} - 48 q^{71} + 16 q^{73} - 52 q^{74} + 16 q^{75} + 4 q^{76} - 8 q^{77} + 72 q^{78} + 4 q^{79} + 8 q^{80} + 136 q^{82} - 44 q^{83} - 152 q^{84} + 104 q^{86} + 52 q^{87} - 200 q^{90} + 24 q^{91} - 76 q^{92} + 4 q^{93} + 20 q^{94} + 28 q^{95} - 180 q^{96} - 32 q^{97} - 44 q^{99} + O(q^{100}) \)

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

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