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Properties

Label 1350.2.h
Level $1350$
Weight $2$
Character orbit 1350.h
Rep. character $\chi_{1350}(271,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $160$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1350.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1350, [\chi])\).

Total New Old
Modular forms 1128 160 968
Cusp forms 1032 160 872
Eisenstein series 96 0 96

Trace form

\( 160 q - 40 q^{4} - 4 q^{7} + O(q^{10}) \) \( 160 q - 40 q^{4} - 4 q^{7} + 6 q^{10} + 8 q^{13} - 40 q^{16} + 12 q^{19} + 8 q^{22} + 18 q^{25} + 6 q^{28} + 6 q^{31} - 24 q^{34} - 32 q^{37} + 6 q^{40} + 56 q^{43} + 12 q^{46} + 220 q^{49} + 8 q^{52} + 30 q^{55} + 48 q^{58} + 40 q^{61} - 40 q^{64} - 46 q^{70} + 124 q^{73} - 8 q^{76} + 56 q^{79} + 80 q^{82} - 160 q^{85} - 2 q^{88} + 20 q^{91} - 16 q^{94} - 18 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 3}\)