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Properties

Label 1350.2.bb
Level $1350$
Weight $2$
Character orbit 1350.bb
Rep. character $\chi_{1350}(257,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $648$
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.bb (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 3384 648 2736
Cusp forms 3096 648 2448
Eisenstein series 288 0 288

Trace form

\( 648 q - 24 q^{6} + O(q^{10}) \) \( 648 q - 24 q^{6} - 48 q^{11} - 24 q^{23} - 12 q^{27} + 12 q^{33} + 24 q^{36} + 36 q^{38} + 144 q^{41} + 48 q^{42} + 48 q^{47} + 12 q^{48} + 24 q^{51} + 24 q^{56} + 36 q^{57} - 72 q^{61} - 84 q^{63} + 72 q^{67} - 36 q^{68} + 48 q^{72} + 240 q^{77} - 24 q^{78} + 48 q^{81} + 60 q^{83} + 36 q^{86} + 252 q^{87} + 48 q^{92} + 96 q^{93} + 72 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)