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Properties

Label 1800.2.w
Level $1800$
Weight $2$
Character orbit 1800.w
Rep. character $\chi_{1800}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $176$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1800.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1800, [\chi])\).

Total New Old
Modular forms 768 184 584
Cusp forms 672 176 496
Eisenstein series 96 8 88

Trace form

\( 176 q - 2 q^{2} - 8 q^{8} + O(q^{10}) \) \( 176 q - 2 q^{2} - 8 q^{8} + 8 q^{11} - 12 q^{16} + 4 q^{22} + 20 q^{26} - 12 q^{28} - 12 q^{32} + 36 q^{38} + 8 q^{41} + 36 q^{43} + 8 q^{46} + 4 q^{52} + 88 q^{56} + 60 q^{58} + 24 q^{62} + 28 q^{67} + 68 q^{68} - 16 q^{73} - 12 q^{76} + 60 q^{82} + 36 q^{83} - 40 q^{86} + 48 q^{88} + 56 q^{91} + 36 q^{92} + 16 q^{97} - 94 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)