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Properties

Label 2.86
Level 2
Weight 86
Dimension 8
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 21
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 86 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(21\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{86}(\Gamma_1(2))\).

Total New Old
Modular forms 22 8 14
Cusp forms 20 8 12
Eisenstein series 2 0 2

Trace form

\( 8 q + 26\!\cdots\!00 q^{3} + 15\!\cdots\!28 q^{4} + 14\!\cdots\!00 q^{5} + 82\!\cdots\!52 q^{6} - 61\!\cdots\!00 q^{7} + 11\!\cdots\!24 q^{9} + 46\!\cdots\!00 q^{10} - 10\!\cdots\!84 q^{11} + 52\!\cdots\!00 q^{12}+ \cdots - 13\!\cdots\!52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{86}^{\mathrm{new}}(\Gamma_1(2))\)

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
2.86.a \(\chi_{2}(1, \cdot)\) 2.86.a.a 4 1
2.86.a.b 4

Decomposition of \(S_{86}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{86}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{86}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)