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Properties

Label 1191.1
Level 1191
Weight 1
Dimension 75
Nonzero newspaces 7
Newform subspaces 12
Sturm bound 105072
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1191 = 3 \cdot 397 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 12 \)
Sturm bound: \(105072\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1191))\).

Total New Old
Modular forms 867 469 398
Cusp forms 75 75 0
Eisenstein series 792 394 398

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 75 0 0 0

Trace form

\( 75 q - 3 q^{3} + 9 q^{4} - 2 q^{7} + 9 q^{9} + O(q^{10}) \) \( 75 q - 3 q^{3} + 9 q^{4} - 2 q^{7} + 9 q^{9} - 4 q^{10} - 3 q^{12} - 2 q^{13} + 5 q^{16} - 6 q^{19} - 2 q^{21} + 9 q^{25} - 3 q^{27} - 2 q^{28} - 4 q^{30} - 6 q^{31} - 4 q^{34} + 9 q^{36} - 2 q^{37} - 2 q^{39} - 8 q^{40} - 2 q^{43} - 7 q^{48} + 7 q^{49} - 2 q^{52} - 6 q^{57} - 2 q^{61} - 2 q^{63} + 5 q^{64} - 2 q^{67} - 6 q^{73} - 3 q^{75} - 6 q^{76} - 2 q^{79} + 9 q^{81} - 4 q^{82} - 2 q^{84} - 4 q^{85} - 4 q^{90} - 4 q^{91} - 6 q^{93} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1191))\)

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
1191.1.c \(\chi_{1191}(398, \cdot)\) None 0 1
1191.1.d \(\chi_{1191}(1190, \cdot)\) 1191.1.d.a 1 1
1191.1.d.b 1
1191.1.d.c 1
1191.1.d.d 2
1191.1.d.e 2
1191.1.d.f 4
1191.1.g \(\chi_{1191}(334, \cdot)\) None 0 2
1191.1.h \(\chi_{1191}(362, \cdot)\) 1191.1.h.a 2 2
1191.1.j \(\chi_{1191}(35, \cdot)\) 1191.1.j.a 2 2
1191.1.m \(\chi_{1191}(157, \cdot)\) None 0 4
1191.1.p \(\chi_{1191}(14, \cdot)\) None 0 6
1191.1.q \(\chi_{1191}(383, \cdot)\) None 0 6
1191.1.r \(\chi_{1191}(107, \cdot)\) 1191.1.r.a 10 10
1191.1.s \(\chi_{1191}(167, \cdot)\) 1191.1.s.a 10 10
1191.1.w \(\chi_{1191}(88, \cdot)\) None 0 12
1191.1.x \(\chi_{1191}(115, \cdot)\) None 0 20
1191.1.z \(\chi_{1191}(65, \cdot)\) 1191.1.z.a 20 20
1191.1.bb \(\chi_{1191}(110, \cdot)\) 1191.1.bb.a 20 20
1191.1.be \(\chi_{1191}(55, \cdot)\) None 0 40
1191.1.bf \(\chi_{1191}(23, \cdot)\) None 0 60
1191.1.bh \(\chi_{1191}(11, \cdot)\) None 0 60
1191.1.bj \(\chi_{1191}(7, \cdot)\) None 0 120