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Properties

Label 1350.2.m
Level $1350$
Weight $2$
Character orbit 1350.m
Rep. character $\chi_{1350}(109,\cdot)$
Character field $\Q(\zeta_{10})$
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.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
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

\( 160 q + 40 q^{4} + O(q^{10}) \) \( 160 q + 40 q^{4} - 10 q^{10} - 40 q^{16} + 12 q^{19} + 20 q^{22} - 26 q^{25} + 10 q^{28} - 6 q^{31} - 24 q^{34} + 40 q^{37} + 10 q^{40} - 12 q^{46} - 100 q^{49} - 58 q^{55} - 40 q^{61} + 40 q^{64} + 40 q^{67} + 98 q^{70} + 8 q^{76} + 56 q^{79} + 144 q^{85} - 10 q^{88} - 20 q^{91} - 16 q^{94} + 10 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)