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Properties

Label 1850.2.z
Level $1850$
Weight $2$
Character orbit 1850.z
Rep. character $\chi_{1850}(121,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $768$
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.z (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 925 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(570\)

Dimensions

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

Total New Old
Modular forms 2304 768 1536
Cusp forms 2240 768 1472
Eisenstein series 64 0 64

Trace form

\( 768 q + 2 q^{2} - 4 q^{3} + 96 q^{4} - 17 q^{5} - 4 q^{8} + 96 q^{9} + O(q^{10}) \) \( 768 q + 2 q^{2} - 4 q^{3} + 96 q^{4} - 17 q^{5} - 4 q^{8} + 96 q^{9} + 6 q^{10} - 8 q^{11} + 6 q^{12} + 12 q^{13} - 4 q^{15} + 96 q^{16} - 2 q^{17} - 40 q^{18} + 8 q^{20} + 8 q^{21} - 24 q^{22} + 8 q^{23} - 55 q^{25} + 72 q^{26} - 28 q^{27} + 12 q^{29} + 28 q^{30} - 48 q^{31} - 8 q^{32} - 4 q^{33} + 23 q^{34} - 16 q^{35} - 192 q^{36} - q^{37} + 16 q^{38} - 3 q^{40} + 28 q^{41} - 28 q^{42} - 64 q^{43} + 4 q^{44} + 122 q^{45} + 20 q^{46} + 8 q^{47} - 12 q^{48} - 416 q^{49} + 15 q^{50} + 24 q^{51} + 12 q^{52} - 46 q^{53} - 10 q^{55} + 40 q^{57} - 14 q^{58} + 6 q^{59} - 12 q^{60} + 14 q^{61} + 10 q^{62} - 192 q^{64} + 13 q^{65} + 32 q^{66} + 58 q^{67} + 4 q^{68} + 38 q^{69} + 4 q^{70} + 8 q^{71} + 10 q^{72} - 28 q^{74} + 272 q^{75} - 148 q^{77} - 30 q^{78} - 6 q^{80} + 78 q^{81} + 52 q^{82} - 16 q^{84} + 66 q^{85} + 20 q^{86} - 2 q^{87} - 32 q^{88} - 11 q^{89} + 59 q^{90} - 12 q^{91} + 6 q^{92} + 108 q^{93} - 32 q^{95} + 68 q^{97} + 10 q^{98} + 16 q^{99} + O(q^{100}) \)

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

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