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Properties

Label 2151.2.y
Level $2151$
Weight $2$
Character orbit 2151.y
Rep. character $\chi_{2151}(55,\cdot)$
Character field $\Q(\zeta_{119})$
Dimension $9504$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2151.y (of order \(119\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 239 \)
Character field: \(\Q(\zeta_{119})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 23424 9696 13728
Cusp forms 22656 9504 13152
Eisenstein series 768 192 576

Trace form

\( 9504 q + 102 q^{2} + 6 q^{4} + 95 q^{5} - 94 q^{7} + 87 q^{8} + O(q^{10}) \) \( 9504 q + 102 q^{2} + 6 q^{4} + 95 q^{5} - 94 q^{7} + 87 q^{8} - 76 q^{10} + 59 q^{11} - 94 q^{13} + 81 q^{14} - 64 q^{16} + 91 q^{17} - 101 q^{19} + 142 q^{20} - 135 q^{22} + 138 q^{23} - 24 q^{25} + 109 q^{26} - 218 q^{28} + 105 q^{29} - 99 q^{31} + 194 q^{32} - 141 q^{34} + 137 q^{35} - 101 q^{37} - 10 q^{38} - 8 q^{40} + 110 q^{41} - 115 q^{43} + 127 q^{44} - 51 q^{46} + 146 q^{47} + 7 q^{49} + 138 q^{50} - 82 q^{52} + 60 q^{53} - 211 q^{55} + 26 q^{56} + 94 q^{58} + 141 q^{59} - 115 q^{61} + 138 q^{62} + 41 q^{64} + 143 q^{65} - 76 q^{67} + 223 q^{68} - 382 q^{70} - 20 q^{71} - 155 q^{73} + 63 q^{74} + 22 q^{76} + 391 q^{77} - 75 q^{79} + 47 q^{80} - 88 q^{82} - 31 q^{83} + 97 q^{85} + 137 q^{86} + 59 q^{88} + 260 q^{89} - 100 q^{91} - 135 q^{92} - 29 q^{94} - 19 q^{95} - 59 q^{97} + 64 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(2151, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2151, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(239, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(717, [\chi])\)\(^{\oplus 2}\)