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Properties

Label 1950.2.cs
Level $1950$
Weight $2$
Character orbit 1950.cs
Rep. character $\chi_{1950}(113,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2240$
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.cs (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 975 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 6848 2240 4608
Cusp forms 6592 2240 4352
Eisenstein series 256 0 256

Trace form

\( 2240 q + O(q^{10}) \) \( 2240 q - 24 q^{13} - 280 q^{16} + 16 q^{18} + 80 q^{19} - 24 q^{27} - 12 q^{30} - 52 q^{33} + 80 q^{34} + 8 q^{37} + 40 q^{39} + 16 q^{40} - 12 q^{42} + 8 q^{43} - 20 q^{45} - 24 q^{52} - 8 q^{55} + 96 q^{57} - 8 q^{58} + 32 q^{60} + 76 q^{63} - 40 q^{67} + 140 q^{69} - 128 q^{70} + 8 q^{72} + 80 q^{73} - 96 q^{75} - 64 q^{78} + 96 q^{82} - 16 q^{85} - 192 q^{87} + 96 q^{90} + 68 q^{93} + 40 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)