Properties

Label 1850.2.cf
Level $1850$
Weight $2$
Character orbit 1850.cf
Rep. character $\chi_{1850}(17,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $4560$
Sturm bound $570$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1850.cf (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 925 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(570\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1850, [\chi])\).

Total New Old
Modular forms 13872 4560 9312
Cusp forms 13488 4560 8928
Eisenstein series 384 0 384

Trace form

\( 4560 q + 12 q^{3} - 6 q^{8} + O(q^{10}) \) \( 4560 q + 12 q^{3} - 6 q^{8} + 12 q^{12} + 24 q^{20} + 12 q^{25} - 12 q^{27} - 192 q^{30} + 12 q^{33} + 84 q^{35} - 24 q^{37} + 24 q^{40} + 30 q^{41} - 84 q^{42} - 120 q^{45} + 60 q^{50} - 48 q^{53} - 312 q^{57} - 12 q^{58} + 120 q^{59} + 60 q^{61} - 60 q^{62} + 570 q^{64} + 36 q^{65} - 156 q^{67} - 360 q^{69} + 24 q^{70} + 120 q^{71} + 6 q^{73} + 30 q^{74} + 768 q^{75} + 60 q^{77} - 12 q^{80} + 120 q^{81} - 96 q^{83} + 384 q^{87} + 72 q^{88} - 96 q^{92} - 156 q^{93} + 108 q^{95} - 36 q^{97} - 24 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1850, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(925, [\chi])\)\(^{\oplus 2}\)