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Properties

Label 2601.2.bk
Level $2601$
Weight $2$
Character orbit 2601.bk
Rep. character $\chi_{2601}(25,\cdot)$
Character field $\Q(\zeta_{408})$
Dimension $38912$
Sturm bound $612$

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Defining parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.bk (of order \(408\) and degree \(128\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2601 \)
Character field: \(\Q(\zeta_{408})\)
Sturm bound: \(612\)

Dimensions

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

Total New Old
Modular forms 39424 39424 0
Cusp forms 38912 38912 0
Eisenstein series 512 512 0

Trace form

\( 38912 q - 64 q^{2} - 128 q^{3} - 68 q^{4} - 64 q^{5} - 128 q^{6} - 64 q^{7} - 240 q^{8} - 116 q^{9} + O(q^{10}) \) \( 38912 q - 64 q^{2} - 128 q^{3} - 68 q^{4} - 64 q^{5} - 128 q^{6} - 64 q^{7} - 240 q^{8} - 116 q^{9} - 256 q^{10} - 68 q^{11} - 92 q^{12} - 68 q^{13} - 64 q^{14} - 132 q^{15} - 1252 q^{16} - 256 q^{17} - 120 q^{18} - 256 q^{19} - 32 q^{20} - 136 q^{21} - 64 q^{22} - 76 q^{23} + 516 q^{24} - 64 q^{25} - 240 q^{26} - 104 q^{27} - 224 q^{28} - 64 q^{29} - 136 q^{30} - 64 q^{31} - 96 q^{32} - 120 q^{33} - 88 q^{34} - 368 q^{35} - 92 q^{36} - 256 q^{37} - 380 q^{39} - 80 q^{40} - 88 q^{41} - 184 q^{42} - 52 q^{43} - 288 q^{44} - 132 q^{45} - 304 q^{46} - 68 q^{47} - 112 q^{48} - 64 q^{49} - 116 q^{50} - 96 q^{51} + 4 q^{52} - 288 q^{53} - 224 q^{54} - 272 q^{55} + 8 q^{56} - 200 q^{57} - 64 q^{58} - 124 q^{59} - 128 q^{60} - 64 q^{61} - 1072 q^{62} - 220 q^{63} - 272 q^{64} - 16 q^{65} - 312 q^{66} - 60 q^{67} - 80 q^{68} - 120 q^{69} - 56 q^{70} - 320 q^{71} - 136 q^{72} - 256 q^{73} - 120 q^{74} - 120 q^{75} - 336 q^{76} - 76 q^{77} - 64 q^{78} - 64 q^{79} - 264 q^{80} - 136 q^{81} - 136 q^{82} - 112 q^{83} - 128 q^{84} - 16 q^{85} + 20 q^{86} - 84 q^{87} - 68 q^{88} - 272 q^{89} - 336 q^{90} - 248 q^{91} - 144 q^{92} - 132 q^{93} - 48 q^{94} - 40 q^{95} - 316 q^{96} - 100 q^{97} - 272 q^{98} - 180 q^{99} + O(q^{100}) \)

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.