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Properties

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

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

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 available newforms together with their dimension.

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