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Properties

Label 1127.1
Level 1127
Weight 1
Dimension 82
Nonzero newspaces 5
Newform subspaces 14
Sturm bound 103488
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1127 = 7^{2} \cdot 23 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 14 \)
Sturm bound: \(103488\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1127))\).

Total New Old
Modular forms 1425 1101 324
Cusp forms 105 82 23
Eisenstein series 1320 1019 301

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 82 0 0 0

Trace form

\( 82 q + 3 q^{2} + q^{3} + 3 q^{4} - q^{6} - 9 q^{8} + q^{9} + O(q^{10}) \) \( 82 q + 3 q^{2} + q^{3} + 3 q^{4} - q^{6} - 9 q^{8} + q^{9} + 2 q^{11} + q^{13} - 5 q^{16} + 2 q^{18} - 8 q^{22} + q^{24} - q^{26} - q^{27} - 15 q^{29} + q^{31} - 5 q^{32} + q^{36} + 2 q^{37} - q^{39} + q^{41} - 4 q^{43} - 5 q^{44} + 3 q^{46} + q^{47} - q^{48} - 14 q^{50} + 2 q^{53} + q^{54} - 8 q^{58} - 2 q^{59} - q^{62} - 21 q^{64} + 2 q^{67} + q^{69} - 15 q^{71} + 4 q^{72} + q^{73} - 7 q^{74} + q^{75} - 23 q^{78} + 2 q^{79} + 2 q^{81} - q^{82} + 4 q^{86} - q^{87} - 3 q^{88} - 24 q^{92} - q^{93} - q^{94} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1127))\)

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
1127.1.b \(\chi_{1127}(783, \cdot)\) None 0 1
1127.1.d \(\chi_{1127}(344, \cdot)\) 1127.1.d.a 1 1
1127.1.d.b 1
1127.1.d.c 2
1127.1.d.d 2
1127.1.d.e 4
1127.1.f \(\chi_{1127}(275, \cdot)\) 1127.1.f.a 2 2
1127.1.f.b 2
1127.1.f.c 2
1127.1.f.d 4
1127.1.f.e 4
1127.1.f.f 8
1127.1.h \(\chi_{1127}(668, \cdot)\) None 0 2
1127.1.k \(\chi_{1127}(22, \cdot)\) None 0 6
1127.1.m \(\chi_{1127}(139, \cdot)\) None 0 6
1127.1.o \(\chi_{1127}(99, \cdot)\) 1127.1.o.a 10 10
1127.1.q \(\chi_{1127}(48, \cdot)\) None 0 10
1127.1.s \(\chi_{1127}(24, \cdot)\) None 0 12
1127.1.u \(\chi_{1127}(114, \cdot)\) None 0 12
1127.1.v \(\chi_{1127}(31, \cdot)\) 1127.1.v.a 20 20
1127.1.x \(\chi_{1127}(30, \cdot)\) 1127.1.x.a 20 20
1127.1.z \(\chi_{1127}(6, \cdot)\) None 0 60
1127.1.bb \(\chi_{1127}(15, \cdot)\) None 0 60
1127.1.bd \(\chi_{1127}(11, \cdot)\) None 0 120
1127.1.bf \(\chi_{1127}(3, \cdot)\) None 0 120

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1127))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1127)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)