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Properties

Label 1350.2.w
Level $1350$
Weight $2$
Character orbit 1350.w
Rep. character $\chi_{1350}(53,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $320$
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.w (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 2256 320 1936
Cusp forms 2064 320 1744
Eisenstein series 192 0 192

Trace form

\( 320 q + 4 q^{7} + O(q^{10}) \) \( 320 q + 4 q^{7} - 4 q^{10} - 24 q^{13} + 80 q^{16} - 40 q^{19} - 36 q^{22} - 8 q^{25} - 16 q^{28} + 80 q^{34} - 24 q^{37} + 16 q^{40} + 72 q^{43} + 24 q^{52} + 12 q^{55} - 16 q^{58} + 72 q^{67} + 76 q^{70} + 28 q^{73} + 80 q^{79} + 48 q^{82} + 176 q^{85} + 4 q^{88} - 8 q^{97} + O(q^{100}) \)

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

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