Properties

Label 2601.2.be
Level $2601$
Weight $2$
Character orbit 2601.be
Rep. character $\chi_{2601}(19,\cdot)$
Character field $\Q(\zeta_{136})$
Dimension $8128$
Sturm bound $612$

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Defining parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.be (of order \(136\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{136})\)
Sturm bound: \(612\)

Dimensions

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

Total New Old
Modular forms 19840 8256 11584
Cusp forms 19328 8128 11200
Eisenstein series 512 128 384

Trace form

\( 8128q + 64q^{2} - 68q^{4} + 60q^{5} - 64q^{7} + 72q^{8} + O(q^{10}) \) \( 8128q + 64q^{2} - 68q^{4} + 60q^{5} - 64q^{7} + 72q^{8} - 64q^{10} + 72q^{11} - 68q^{13} + 56q^{14} + 448q^{16} + 60q^{17} - 44q^{19} + 88q^{20} - 32q^{22} + 80q^{23} - 72q^{25} + 80q^{26} - 120q^{28} + 64q^{29} - 72q^{31} + 72q^{32} - 32q^{34} + 92q^{35} - 68q^{37} - 156q^{40} + 40q^{41} - 44q^{43} + 48q^{44} - 88q^{46} + 68q^{47} - 92q^{49} + 32q^{50} - 116q^{52} + 32q^{53} - 68q^{55} + 32q^{56} - 4q^{58} + 84q^{59} - 20q^{61} - 336q^{62} - 68q^{64} + 88q^{65} - 44q^{67} + 80q^{68} + 36q^{70} + 72q^{71} - 16q^{73} + 152q^{74} + 60q^{76} + 756q^{77} - 64q^{79} + 52q^{80} + 16q^{82} + 116q^{83} - 60q^{85} + 68q^{86} - 240q^{88} + 68q^{89} - 100q^{91} + 280q^{92} - 156q^{94} + 20q^{95} - 108q^{97} + 68q^{98} + O(q^{100}) \)

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

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