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Properties

Label 1950.2.v
Level $1950$
Weight $2$
Character orbit 1950.v
Rep. character $\chi_{1950}(391,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $240$
Sturm bound $840$

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Defining parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.v (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1950, [\chi])\).

Total New Old
Modular forms 1712 240 1472
Cusp forms 1648 240 1408
Eisenstein series 64 0 64

Trace form

\( 240 q - 60 q^{4} - 8 q^{5} - 4 q^{6} - 24 q^{7} - 60 q^{9} + O(q^{10}) \) \( 240 q - 60 q^{4} - 8 q^{5} - 4 q^{6} - 24 q^{7} - 60 q^{9} - 4 q^{10} + 24 q^{11} - 4 q^{15} - 60 q^{16} + 24 q^{17} - 8 q^{19} - 8 q^{20} - 8 q^{21} + 16 q^{22} + 48 q^{23} + 16 q^{24} - 28 q^{25} - 4 q^{28} + 24 q^{29} + 32 q^{30} + 12 q^{31} - 8 q^{33} - 16 q^{34} - 60 q^{36} - 16 q^{37} - 32 q^{38} - 4 q^{40} + 12 q^{42} + 96 q^{43} - 16 q^{44} - 8 q^{45} + 8 q^{46} + 32 q^{47} + 216 q^{49} - 32 q^{50} + 24 q^{53} - 4 q^{54} + 24 q^{55} - 48 q^{57} - 8 q^{58} + 48 q^{59} + 16 q^{60} + 32 q^{61} - 32 q^{62} + 16 q^{63} - 60 q^{64} - 8 q^{65} + 48 q^{67} - 16 q^{68} - 12 q^{70} + 48 q^{71} + 24 q^{73} - 32 q^{75} + 32 q^{76} - 32 q^{77} + 24 q^{79} - 8 q^{80} - 60 q^{81} - 32 q^{82} + 64 q^{83} - 8 q^{84} + 32 q^{85} - 8 q^{87} - 4 q^{88} - 48 q^{89} - 4 q^{90} - 8 q^{91} - 32 q^{92} + 32 q^{93} - 8 q^{95} - 4 q^{96} + 52 q^{97} - 32 q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1950, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)