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

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

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

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