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Properties

Label 2601.2.ba
Level $2601$
Weight $2$
Character orbit 2601.ba
Rep. character $\chi_{2601}(55,\cdot)$
Character field $\Q(\zeta_{68})$
Dimension $4032$
Sturm bound $612$

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Defining parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.ba (of order \(68\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{68})\)
Sturm bound: \(612\)

Dimensions

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

Total New Old
Modular forms 9920 4096 5824
Cusp forms 9664 4032 5632
Eisenstein series 256 64 192

Trace form

\( 4032 q + 34 q^{2} + 218 q^{4} + 30 q^{5} - 34 q^{7} + 34 q^{8} + O(q^{10}) \) \( 4032 q + 34 q^{2} + 218 q^{4} + 30 q^{5} - 34 q^{7} + 34 q^{8} - 98 q^{10} + 34 q^{11} - 30 q^{13} + 58 q^{14} - 270 q^{16} + 30 q^{17} - 34 q^{19} + 22 q^{20} - 42 q^{22} + 18 q^{23} + 102 q^{25} + 34 q^{26} - 26 q^{28} + 38 q^{29} - 42 q^{31} + 34 q^{32} - 42 q^{34} + 34 q^{35} - 46 q^{37} - 104 q^{38} - 62 q^{40} + 62 q^{41} - 34 q^{43} + 2 q^{44} - 170 q^{46} + 30 q^{47} - 34 q^{49} - 14 q^{50} - 2 q^{52} + 68 q^{53} - 46 q^{55} + 10 q^{56} - 62 q^{58} + 34 q^{59} - 30 q^{61} + 254 q^{62} + 210 q^{64} + 50 q^{65} - 126 q^{67} + 94 q^{68} - 34 q^{70} + 58 q^{71} - 22 q^{73} + 6 q^{74} - 102 q^{76} - 306 q^{77} + 68 q^{79} + 94 q^{80} - 38 q^{82} + 170 q^{83} - 40 q^{85} + 38 q^{86} + 186 q^{88} + 38 q^{89} + 6 q^{91} + 158 q^{92} - 306 q^{94} + 42 q^{95} - 62 q^{97} - 14 q^{98} + O(q^{100}) \)

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

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