↑

Properties

Label 2365.2.dn
Level $2365$
Weight $2$
Character orbit 2365.dn
Rep. character $\chi_{2365}(46,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $8448$
Sturm bound $528$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2365 = 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2365.dn (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 473 \)
Character field: \(\Q(\zeta_{210})\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2365, [\chi])\).

Total New Old
Modular forms 12864 8448 4416
Cusp forms 12480 8448 4032
Eisenstein series 384 0 384

Trace form

\( 8448 q + 344 q^{4} + 20 q^{6} - 140 q^{8} + 152 q^{9} + O(q^{10}) \) \( 8448 q + 344 q^{4} + 20 q^{6} - 140 q^{8} + 152 q^{9} - 4 q^{11} + 10 q^{13} - 10 q^{14} + 316 q^{16} - 150 q^{18} + 120 q^{19} + 16 q^{20} - 42 q^{22} - 92 q^{23} + 150 q^{24} + 176 q^{25} + 28 q^{26} - 150 q^{28} + 12 q^{31} - 42 q^{33} - 252 q^{34} - 992 q^{36} - 216 q^{37} - 8 q^{38} + 212 q^{44} - 30 q^{46} + 40 q^{47} + 1048 q^{49} - 124 q^{53} - 124 q^{56} + 30 q^{57} - 82 q^{58} - 96 q^{59} - 42 q^{60} + 184 q^{64} + 62 q^{66} + 24 q^{67} - 650 q^{68} + 144 q^{69} - 56 q^{70} + 88 q^{71} - 30 q^{74} - 84 q^{75} - 54 q^{77} + 120 q^{78} - 80 q^{79} - 24 q^{80} - 186 q^{81} - 50 q^{83} + 480 q^{84} - 518 q^{86} + 70 q^{88} + 112 q^{89} + 24 q^{91} + 152 q^{92} - 426 q^{93} + 840 q^{94} - 130 q^{96} + 64 q^{97} - 14 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2365, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2365, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2365, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(473, [\chi])\)\(^{\oplus 2}\)