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Properties

Label 2151.2.u
Level $2151$
Weight $2$
Character orbit 2151.u
Rep. character $\chi_{2151}(22,\cdot)$
Character field $\Q(\zeta_{51})$
Dimension $7616$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2151.u (of order \(51\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2151 \)
Character field: \(\Q(\zeta_{51})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2151, [\chi])\).

Total New Old
Modular forms 7744 7744 0
Cusp forms 7616 7616 0
Eisenstein series 128 128 0

Trace form

\( 7616 q - 15 q^{2} - 30 q^{3} + 221 q^{4} - 15 q^{5} - 40 q^{6} - 15 q^{7} - 80 q^{8} - 22 q^{9} + O(q^{10}) \) \( 7616 q - 15 q^{2} - 30 q^{3} + 221 q^{4} - 15 q^{5} - 40 q^{6} - 15 q^{7} - 80 q^{8} - 22 q^{9} - 136 q^{10} - 45 q^{11} - 38 q^{12} - 15 q^{13} - 21 q^{14} - 30 q^{15} + 221 q^{16} - 72 q^{17} - 58 q^{18} - 60 q^{19} - 61 q^{20} - 96 q^{21} - 23 q^{22} - 19 q^{23} - 36 q^{24} + 215 q^{25} - 52 q^{26} - 48 q^{27} - 84 q^{28} - 17 q^{29} - 106 q^{30} - 15 q^{31} - 3 q^{32} - 52 q^{33} - 11 q^{34} - 68 q^{35} - 60 q^{36} - 60 q^{37} + 184 q^{38} - 400 q^{39} - 73 q^{40} - 31 q^{41} + 76 q^{42} - 15 q^{43} - 164 q^{44} + 169 q^{45} - 68 q^{46} - 25 q^{47} - 12 q^{48} + 211 q^{49} - 88 q^{50} - 88 q^{51} - 9 q^{52} - 12 q^{53} - 516 q^{54} - 80 q^{55} - 29 q^{56} - 32 q^{57} - 5 q^{58} - 17 q^{59} + 57 q^{60} - 15 q^{61} - 70 q^{62} - 40 q^{63} - 568 q^{64} - 43 q^{65} + 66 q^{66} - 15 q^{67} - 33 q^{68} - 220 q^{69} - 136 q^{70} - 72 q^{71} + 111 q^{72} - 60 q^{73} - 59 q^{74} - 56 q^{75} + 53 q^{76} - 63 q^{77} - 434 q^{78} - 3 q^{79} - 556 q^{80} + 50 q^{81} - 104 q^{82} - 29 q^{83} - 42 q^{84} + 7 q^{85} - 7 q^{86} + 12 q^{87} - 69 q^{88} - 56 q^{89} - 253 q^{90} - 112 q^{91} - 211 q^{92} + 184 q^{93} - 29 q^{94} + 127 q^{95} + 61 q^{96} - 15 q^{97} - 256 q^{98} + 394 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2151, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.