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Properties

Label 1950.2.n
Level $1950$
Weight $2$
Character orbit 1950.n
Rep. character $\chi_{1950}(749,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $168$
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.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 195 \)
Character field: \(\Q(i)\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 888 168 720
Cusp forms 792 168 624
Eisenstein series 96 0 96

Trace form

\( 168 q + O(q^{10}) \) \( 168 q - 168 q^{16} - 8 q^{19} - 16 q^{21} + 24 q^{31} + 32 q^{34} + 32 q^{39} - 16 q^{46} + 24 q^{54} - 64 q^{61} + 32 q^{66} + 8 q^{76} + 128 q^{79} - 64 q^{81} - 16 q^{84} + 24 q^{91} - 128 q^{94} - 72 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)