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Properties

Label 2601.2.n
Level $2601$
Weight $2$
Character orbit 2601.n
Rep. character $\chi_{2601}(616,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1024$
Sturm bound $612$

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Defining parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.n (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 153 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(612\)

Dimensions

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

Total New Old
Modular forms 1296 1136 160
Cusp forms 1152 1024 128
Eisenstein series 144 112 32

Trace form

\( 1024 q + 6 q^{3} + 488 q^{4} + 2 q^{5} + 10 q^{6} + 2 q^{7} + O(q^{10}) \) \( 1024 q + 6 q^{3} + 488 q^{4} + 2 q^{5} + 10 q^{6} + 2 q^{7} + 16 q^{10} + 24 q^{12} + 4 q^{13} - 432 q^{16} - 64 q^{18} - 18 q^{20} + 4 q^{22} + 8 q^{23} + 2 q^{24} + 10 q^{29} + 56 q^{30} + 2 q^{31} - 20 q^{33} + 8 q^{37} + 88 q^{38} - 34 q^{39} + 20 q^{40} - 32 q^{41} - 20 q^{44} - 20 q^{45} + 40 q^{46} + 64 q^{47} - 62 q^{48} - 88 q^{50} - 68 q^{52} + 46 q^{54} + 16 q^{55} - 12 q^{56} - 72 q^{57} + 10 q^{58} + 2 q^{61} + 28 q^{62} - 64 q^{63} - 632 q^{64} - 8 q^{65} + 4 q^{67} + 8 q^{69} + 84 q^{71} - 92 q^{72} + 44 q^{73} + 14 q^{74} - 46 q^{75} + 56 q^{78} - 10 q^{79} - 204 q^{80} - 52 q^{81} + 52 q^{82} + 164 q^{84} - 44 q^{86} - 16 q^{88} - 128 q^{89} + 66 q^{90} - 44 q^{91} - 136 q^{92} - 4 q^{95} + 2 q^{96} + 44 q^{97} - 240 q^{98} - 6 q^{99} + O(q^{100}) \)

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

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