Properties

Label 7.3
Level 7
Weight 3
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 12
Trace bound 0

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 7 7 0
Cusp forms 1 1 0
Eisenstein series 6 6 0

Trace form

\( q - 3 q^{2} + 5 q^{4} - 7 q^{7} - 3 q^{8} + 9 q^{9} + O(q^{10}) \) \( q - 3 q^{2} + 5 q^{4} - 7 q^{7} - 3 q^{8} + 9 q^{9} - 6 q^{11} + 21 q^{14} - 11 q^{16} - 27 q^{18} + 18 q^{22} + 18 q^{23} + 25 q^{25} - 35 q^{28} - 54 q^{29} + 45 q^{32} + 45 q^{36} - 38 q^{37} + 58 q^{43} - 30 q^{44} - 54 q^{46} + 49 q^{49} - 75 q^{50} - 6 q^{53} + 21 q^{56} + 162 q^{58} - 63 q^{63} - 91 q^{64} - 118 q^{67} + 114 q^{71} - 27 q^{72} + 114 q^{74} + 42 q^{77} - 94 q^{79} + 81 q^{81} - 174 q^{86} + 18 q^{88} + 90 q^{92} - 147 q^{98} - 54 q^{99} + O(q^{100}) \)

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

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
7.3.b \(\chi_{7}(6, \cdot)\) 7.3.b.a 1 1
7.3.d \(\chi_{7}(3, \cdot)\) None 0 2