↑

Properties

Label 2151.2.m
Level $2151$
Weight $2$
Character orbit 2151.m
Rep. character $\chi_{2151}(163,\cdot)$
Character field $\Q(\zeta_{17})$
Dimension $1584$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2151.m (of order \(17\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 239 \)
Character field: \(\Q(\zeta_{17})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 3904 1616 2288
Cusp forms 3776 1584 2192
Eisenstein series 128 32 96

Trace form

\( 1584 q + 17 q^{2} - 111 q^{4} + 17 q^{5} - 11 q^{7} + 11 q^{8} + O(q^{10}) \) \( 1584 q + 17 q^{2} - 111 q^{4} + 17 q^{5} - 11 q^{7} + 11 q^{8} - 36 q^{10} + 53 q^{11} - 11 q^{13} + 3 q^{14} - 41 q^{16} - 11 q^{19} - 30 q^{20} - 26 q^{22} - 19 q^{23} - 116 q^{25} + 3 q^{26} + 141 q^{28} + 21 q^{29} - 13 q^{31} - 5 q^{32} - 27 q^{34} - 11 q^{35} - 11 q^{37} + 136 q^{38} - 97 q^{40} + 23 q^{41} - 67 q^{43} + 20 q^{44} - 47 q^{46} + q^{47} - 140 q^{49} - 5 q^{50} + 19 q^{52} + 17 q^{53} + 106 q^{55} - 19 q^{56} - 136 q^{58} - 71 q^{59} - 25 q^{61} + 2 q^{62} - 125 q^{64} - 31 q^{65} - 29 q^{67} - 76 q^{68} + 172 q^{70} + 13 q^{71} - 62 q^{73} - 7 q^{74} + 13 q^{76} - 279 q^{77} - 65 q^{79} + 170 q^{80} - 24 q^{82} + 73 q^{83} - 195 q^{85} + 45 q^{86} - 45 q^{88} - 120 q^{89} + 9 q^{91} + 233 q^{92} - 27 q^{94} + 54 q^{95} - 32 q^{97} + 76 q^{98} + O(q^{100}) \)

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

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