Properties

Label 1755.2.fk
Level $1755$
Weight $2$
Character orbit 1755.fk
Rep. character $\chi_{1755}(38,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $2976$
Sturm bound $504$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1755.fk (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1755 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1755, [\chi])\).

Total New Old
Modular forms 3072 3072 0
Cusp forms 2976 2976 0
Eisenstein series 96 96 0

Trace form

\( 2976 q - 24 q^{3} + O(q^{10}) \) \( 2976 q - 24 q^{3} - 12 q^{10} - 24 q^{12} - 12 q^{13} - 48 q^{16} - 36 q^{17} - 24 q^{22} + 24 q^{23} - 24 q^{25} - 24 q^{27} - 96 q^{30} - 36 q^{35} - 48 q^{36} + 72 q^{38} - 72 q^{40} - 24 q^{42} - 24 q^{43} + 48 q^{48} - 36 q^{52} - 48 q^{55} - 48 q^{56} - 48 q^{61} - 36 q^{62} + 60 q^{65} - 240 q^{66} + 24 q^{68} - 60 q^{75} - 120 q^{77} - 78 q^{78} - 24 q^{81} - 48 q^{82} + 72 q^{87} + 48 q^{88} - 132 q^{90} - 12 q^{91} + 240 q^{92} + 36 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1755, [\chi])\) into newform subspaces

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