Properties

Label 3.7
Level 3
Weight 7
Dimension 1
Nonzero newspaces 1
Newforms 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(3))\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

Trace form

\( q - 27q^{3} + 64q^{4} - 286q^{7} + 729q^{9} + O(q^{10}) \) \( q - 27q^{3} + 64q^{4} - 286q^{7} + 729q^{9} - 1728q^{12} + 506q^{13} + 4096q^{16} - 10582q^{19} + 7722q^{21} + 15625q^{25} - 19683q^{27} - 18304q^{28} + 35282q^{31} + 46656q^{36} - 89206q^{37} - 13662q^{39} + 111386q^{43} - 110592q^{48} - 35853q^{49} + 32384q^{52} + 285714q^{57} - 420838q^{61} - 208494q^{63} + 262144q^{64} + 172874q^{67} + 638066q^{73} - 421875q^{75} - 677248q^{76} - 204622q^{79} + 531441q^{81} + 494208q^{84} - 144716q^{91} - 952614q^{93} - 56446q^{97} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
3.7.b \(\chi_{3}(2, \cdot)\) 3.7.b.a 1 1