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Properties

Label 791.1
Level 791
Weight 1
Dimension 69
Nonzero newspaces 7
Newform subspaces 10
Sturm bound 51072
Trace bound 2

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Defining parameters

Level: \( N \) = \( 791 = 7 \cdot 113 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 10 \)
Sturm bound: \(51072\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(791))\).

Total New Old
Modular forms 741 623 118
Cusp forms 69 69 0
Eisenstein series 672 554 118

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 69 0 0 0

Trace form

\( 69 q - 2 q^{2} + 7 q^{4} - 3 q^{7} - 4 q^{8} + 13 q^{9} + O(q^{10}) \) \( 69 q - 2 q^{2} + 7 q^{4} - 3 q^{7} - 4 q^{8} + 13 q^{9} - 6 q^{11} - 2 q^{14} - 4 q^{15} + q^{16} - 10 q^{18} - 4 q^{22} - 2 q^{23} + 13 q^{25} - 9 q^{28} - 2 q^{29} - 8 q^{30} - 6 q^{32} + 7 q^{36} - 2 q^{37} - 2 q^{43} - 18 q^{44} - 4 q^{46} + 13 q^{49} - 10 q^{50} - 4 q^{51} - 6 q^{53} - 4 q^{56} - 4 q^{57} - 4 q^{58} - 12 q^{60} - 3 q^{63} - 5 q^{64} - 2 q^{67} - 2 q^{71} - 20 q^{72} - 4 q^{74} - 6 q^{77} - 2 q^{79} + 9 q^{81} - 4 q^{85} - 4 q^{86} - 8 q^{88} - 6 q^{92} - 4 q^{95} - 2 q^{98} - 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(791))\)

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
791.1.b \(\chi_{791}(566, \cdot)\) None 0 1
791.1.d \(\chi_{791}(790, \cdot)\) 791.1.d.a 1 1
791.1.d.b 2
791.1.d.c 4
791.1.d.d 8
791.1.g \(\chi_{791}(580, \cdot)\) 791.1.g.a 2 2
791.1.h \(\chi_{791}(451, \cdot)\) None 0 2
791.1.i \(\chi_{791}(227, \cdot)\) None 0 2
791.1.l \(\chi_{791}(69, \cdot)\) 791.1.l.a 4 4
791.1.o \(\chi_{791}(241, \cdot)\) None 0 4
791.1.p \(\chi_{791}(83, \cdot)\) 791.1.p.a 6 6
791.1.r \(\chi_{791}(335, \cdot)\) 791.1.r.a 6 6
791.1.s \(\chi_{791}(71, \cdot)\) None 0 8
791.1.v \(\chi_{791}(131, \cdot)\) None 0 8
791.1.x \(\chi_{791}(111, \cdot)\) 791.1.x.a 12 12
791.1.ba \(\chi_{791}(129, \cdot)\) None 0 12
791.1.bb \(\chi_{791}(117, \cdot)\) None 0 12
791.1.bc \(\chi_{791}(65, \cdot)\) None 0 16
791.1.bf \(\chi_{791}(13, \cdot)\) 791.1.bf.a 24 24
791.1.bg \(\chi_{791}(115, \cdot)\) None 0 24
791.1.bj \(\chi_{791}(29, \cdot)\) None 0 48
791.1.bl \(\chi_{791}(26, \cdot)\) None 0 48
791.1.bn \(\chi_{791}(23, \cdot)\) None 0 96