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Properties

Label 1900.2.bg
Level $1900$
Weight $2$
Character orbit 1900.bg
Rep. character $\chi_{1900}(293,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $120$
Sturm bound $600$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.bg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1900, [\chi])\).

Total New Old
Modular forms 1272 120 1152
Cusp forms 1128 120 1008
Eisenstein series 144 0 144

Trace form

\( 120 q + 4 q^{7} + O(q^{10}) \) \( 120 q + 4 q^{7} + 16 q^{11} - 8 q^{17} + 12 q^{21} - 16 q^{23} + 48 q^{33} - 24 q^{41} + 10 q^{43} - 30 q^{47} + 12 q^{51} - 18 q^{53} + 18 q^{57} + 4 q^{61} + 38 q^{63} + 48 q^{67} - 36 q^{73} + 28 q^{77} + 108 q^{81} + 44 q^{83} + 64 q^{87} - 84 q^{91} + 20 q^{93} - 6 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)