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Properties

Label 2601.2.l
Level $2601$
Weight $2$
Character orbit 2601.l
Rep. character $\chi_{2601}(712,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $420$
Sturm bound $612$

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Defining parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.l (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(612\)

Dimensions

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

Total New Old
Modular forms 1368 476 892
Cusp forms 1080 420 660
Eisenstein series 288 56 232

Trace form

\( 420 q - 4 q^{2} - 8 q^{5} + 4 q^{7} + 4 q^{8} + O(q^{10}) \) \( 420 q - 4 q^{2} - 8 q^{5} + 4 q^{7} + 4 q^{8} + 4 q^{10} + 4 q^{11} - 12 q^{14} - 316 q^{16} + 24 q^{19} + 20 q^{20} + 36 q^{22} + 12 q^{23} - 4 q^{25} + 12 q^{26} - 52 q^{28} - 4 q^{29} - 4 q^{31} + 4 q^{32} + 120 q^{35} - 88 q^{40} - 28 q^{41} + 24 q^{43} - 20 q^{44} - 20 q^{46} - 24 q^{49} + 12 q^{50} - 176 q^{52} - 36 q^{53} - 36 q^{56} + 64 q^{58} + 16 q^{59} + 48 q^{61} + 4 q^{62} + 20 q^{65} + 72 q^{67} + 104 q^{70} + 4 q^{71} + 52 q^{73} + 84 q^{74} - 8 q^{76} + 8 q^{77} + 4 q^{79} - 16 q^{80} + 84 q^{82} + 48 q^{83} + 16 q^{86} - 172 q^{88} - 32 q^{91} - 60 q^{92} - 88 q^{94} - 48 q^{95} - 40 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2601, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(867, [\chi])\)\(^{\oplus 2}\)