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Properties

Label 1850.2.bw
Level $1850$
Weight $2$
Character orbit 1850.bw
Rep. character $\chi_{1850}(23,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1520$
Sturm bound $570$

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Defining parameters

Level: \( N \) \(=\) \( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1850.bw (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 925 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(570\)

Dimensions

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

Total New Old
Modular forms 4624 1520 3104
Cusp forms 4496 1520 2976
Eisenstein series 128 0 128

Trace form

\( 1520 q + 4 q^{3} - 190 q^{4} - 16 q^{5} + O(q^{10}) \) \( 1520 q + 4 q^{3} - 190 q^{4} - 16 q^{5} + 2 q^{10} - 4 q^{12} + 190 q^{16} - 2 q^{17} - 40 q^{18} - 4 q^{20} + 24 q^{22} + 8 q^{25} + 64 q^{27} - 10 q^{29} - 96 q^{30} + 12 q^{33} - 16 q^{35} - 56 q^{37} + 16 q^{40} - 30 q^{41} + 28 q^{42} + 142 q^{45} - 8 q^{47} + 32 q^{48} - 32 q^{50} - 72 q^{53} + 88 q^{55} - 120 q^{57} - 24 q^{58} - 100 q^{59} + 20 q^{60} + 100 q^{61} - 20 q^{62} + 380 q^{64} + 12 q^{65} + 140 q^{67} - 4 q^{68} + 120 q^{69} - 8 q^{70} + 120 q^{71} - 10 q^{72} + 4 q^{73} + 20 q^{74} - 520 q^{75} + 36 q^{77} + 20 q^{78} - 8 q^{80} - 230 q^{81} + 48 q^{82} + 32 q^{83} - 212 q^{87} - 32 q^{88} + 30 q^{89} - 40 q^{90} - 28 q^{92} + 60 q^{93} + 44 q^{95} - 64 q^{97} + 10 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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