Properties

Label 18.26
Level 18
Weight 26
Dimension 60
Nonzero newspaces 2
Newform subspaces 9
Sturm bound 468
Trace bound 1

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 26 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 9 \)
Sturm bound: \(468\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(18))\).

Total New Old
Modular forms 233 60 173
Cusp forms 217 60 157
Eisenstein series 16 0 16

Trace form

\( 60 q - 4096 q^{2} + 53637 q^{3} - 251658240 q^{4} - 481593492 q^{5} - 5612752896 q^{6} - 11577984882 q^{7} + 137438953472 q^{8} - 2488574633973 q^{9} + 2866670075904 q^{10} - 20838120149949 q^{11} - 30186909204480 q^{12}+ \cdots + 53\!\cdots\!34 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(18))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
18.26.a \(\chi_{18}(1, \cdot)\) 18.26.a.a 1 1
18.26.a.b 1
18.26.a.c 1
18.26.a.d 1
18.26.a.e 2
18.26.a.f 2
18.26.a.g 2
18.26.c \(\chi_{18}(7, \cdot)\) 18.26.c.a 24 2
18.26.c.b 26

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)