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Properties

Label 2601.2.q
Level $2601$
Weight $2$
Character orbit 2601.q
Rep. character $\chi_{2601}(154,\cdot)$
Character field $\Q(\zeta_{17})$
Dimension $2016$
Sturm bound $612$

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Defining parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.q (of order \(17\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{17})\)
Sturm bound: \(612\)

Dimensions

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

Total New Old
Modular forms 4960 2048 2912
Cusp forms 4832 2016 2816
Eisenstein series 128 32 96

Trace form

\( 2016 q + 15 q^{2} - 143 q^{4} - 13 q^{5} - 13 q^{7} + 11 q^{8} + O(q^{10}) \) \( 2016 q + 15 q^{2} - 143 q^{4} - 13 q^{5} - 13 q^{7} + 11 q^{8} + 21 q^{10} + 13 q^{11} - 7 q^{13} + 98 q^{14} - 135 q^{16} + 19 q^{17} - 11 q^{19} + 29 q^{20} - 21 q^{22} + 21 q^{23} - 201 q^{25} + 29 q^{26} - 13 q^{28} + 29 q^{29} - 29 q^{31} + 13 q^{32} - 19 q^{34} - 7 q^{35} - 29 q^{37} + 92 q^{38} - 6 q^{40} + 5 q^{41} - 15 q^{43} - 39 q^{44} + 31 q^{46} - 22 q^{47} - 137 q^{49} - 3 q^{50} - 82 q^{52} + 10 q^{53} - 11 q^{55} + 29 q^{56} - 140 q^{58} + 11 q^{59} - 29 q^{61} + 99 q^{62} - 115 q^{64} + 34 q^{65} - 10 q^{67} + 23 q^{68} - 9 q^{70} - 107 q^{71} - 5 q^{73} - 150 q^{74} - 83 q^{76} - 131 q^{77} + 4 q^{79} - 75 q^{80} + 3 q^{82} - 71 q^{83} - 204 q^{85} - 5 q^{86} + 21 q^{88} + 27 q^{89} - 101 q^{91} - 189 q^{92} + 361 q^{94} + q^{95} - 5 q^{97} + 205 q^{98} + O(q^{100}) \)

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

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