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Properties

Label 1950.2.bz
Level $1950$
Weight $2$
Character orbit 1950.bz
Rep. character $\chi_{1950}(77,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1120$
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.bz (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 975 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 3424 1120 2304
Cusp forms 3296 1120 2176
Eisenstein series 128 0 128

Trace form

\( 1120 q + O(q^{10}) \) \( 1120 q + 280 q^{16} - 12 q^{27} - 12 q^{30} - 40 q^{39} + 16 q^{40} + 12 q^{42} - 16 q^{43} - 16 q^{55} + 280 q^{69} - 76 q^{75} + 100 q^{78} + 64 q^{82} - 128 q^{87} - 48 q^{90} + O(q^{100}) \)

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

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