Properties

Label 1800.4.w
Level $1800$
Weight $4$
Character orbit 1800.w
Rep. character $\chi_{1800}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $536$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1800.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1800, [\chi])\).

Total New Old
Modular forms 2208 544 1664
Cusp forms 2112 536 1576
Eisenstein series 96 8 88

Trace form

\( 536 q - 2 q^{2} + 40 q^{8} + O(q^{10}) \) \( 536 q - 2 q^{2} + 40 q^{8} + 8 q^{11} + 372 q^{16} - 56 q^{17} + 364 q^{22} - 908 q^{26} + 244 q^{28} + 628 q^{32} + 596 q^{38} + 8 q^{41} - 860 q^{43} + 1472 q^{46} - 92 q^{52} - 904 q^{56} - 20 q^{58} - 272 q^{62} + 1852 q^{67} - 268 q^{68} + 744 q^{73} - 380 q^{76} + 1756 q^{82} - 2684 q^{83} + 2112 q^{86} + 3056 q^{88} + 3384 q^{91} + 932 q^{92} - 2392 q^{97} + 3762 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)