Properties

Label 1519.1
Level 1519
Weight 1
Dimension 71
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 188160
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1519 = 7^{2} \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(188160\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1519))\).

Total New Old
Modular forms 1886 1478 408
Cusp forms 86 71 15
Eisenstein series 1800 1407 393

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 71 0 0 0

Trace form

\( 71 q + q^{2} + 3 q^{4} + q^{5} - 7 q^{8} + 2 q^{9} + O(q^{10}) \) \( 71 q + q^{2} + 3 q^{4} + q^{5} - 7 q^{8} + 2 q^{9} - 13 q^{10} + 4 q^{16} + q^{18} + q^{19} - 30 q^{20} + 3 q^{25} + 2 q^{31} - 12 q^{32} + 3 q^{36} - 13 q^{38} - 11 q^{40} + q^{41} + q^{45} - 14 q^{47} - 12 q^{50} + q^{59} + q^{62} - 4 q^{64} - 14 q^{67} - 9 q^{70} - 5 q^{71} - 13 q^{72} + 6 q^{76} + 56 q^{80} + 2 q^{81} + 5 q^{82} + 5 q^{90} + 2 q^{94} - 13 q^{95} + q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1519))\)

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
1519.1.b \(\chi_{1519}(342, \cdot)\) None 0 1
1519.1.c \(\chi_{1519}(1177, \cdot)\) 1519.1.c.a 1 1
1519.1.c.b 3
1519.1.c.c 3
1519.1.j \(\chi_{1519}(521, \cdot)\) None 0 2
1519.1.k \(\chi_{1519}(863, \cdot)\) None 0 2
1519.1.n \(\chi_{1519}(30, \cdot)\) 1519.1.n.a 2 2
1519.1.n.b 2
1519.1.n.c 6
1519.1.o \(\chi_{1519}(471, \cdot)\) None 0 2
1519.1.p \(\chi_{1519}(962, \cdot)\) None 0 2
1519.1.q \(\chi_{1519}(129, \cdot)\) None 0 2
1519.1.t \(\chi_{1519}(99, \cdot)\) None 0 2
1519.1.u \(\chi_{1519}(1028, \cdot)\) None 0 2
1519.1.x \(\chi_{1519}(97, \cdot)\) None 0 4
1519.1.y \(\chi_{1519}(246, \cdot)\) None 0 4
1519.1.ba \(\chi_{1519}(92, \cdot)\) 1519.1.ba.a 6 6
1519.1.ba.b 12
1519.1.bb \(\chi_{1519}(125, \cdot)\) None 0 6
1519.1.bk \(\chi_{1519}(148, \cdot)\) None 0 8
1519.1.bl \(\chi_{1519}(195, \cdot)\) None 0 8
1519.1.bo \(\chi_{1519}(116, \cdot)\) None 0 8
1519.1.bp \(\chi_{1519}(79, \cdot)\) None 0 8
1519.1.bq \(\chi_{1519}(264, \cdot)\) None 0 8
1519.1.br \(\chi_{1519}(19, \cdot)\) None 0 8
1519.1.bu \(\chi_{1519}(276, \cdot)\) None 0 8
1519.1.bv \(\chi_{1519}(177, \cdot)\) None 0 8
1519.1.bx \(\chi_{1519}(118, \cdot)\) None 0 12
1519.1.by \(\chi_{1519}(57, \cdot)\) None 0 12
1519.1.cb \(\chi_{1519}(180, \cdot)\) None 0 12
1519.1.cc \(\chi_{1519}(94, \cdot)\) None 0 12
1519.1.cd \(\chi_{1519}(37, \cdot)\) None 0 12
1519.1.ce \(\chi_{1519}(123, \cdot)\) 1519.1.ce.a 36 12
1519.1.ch \(\chi_{1519}(130, \cdot)\) None 0 12
1519.1.ci \(\chi_{1519}(5, \cdot)\) None 0 12
1519.1.cj \(\chi_{1519}(15, \cdot)\) None 0 24
1519.1.ck \(\chi_{1519}(132, \cdot)\) None 0 24
1519.1.cq \(\chi_{1519}(44, \cdot)\) None 0 48
1519.1.cr \(\chi_{1519}(38, \cdot)\) None 0 48
1519.1.cu \(\chi_{1519}(10, \cdot)\) None 0 48
1519.1.cv \(\chi_{1519}(33, \cdot)\) None 0 48
1519.1.cw \(\chi_{1519}(11, \cdot)\) None 0 48
1519.1.cx \(\chi_{1519}(23, \cdot)\) None 0 48
1519.1.da \(\chi_{1519}(20, \cdot)\) None 0 48
1519.1.db \(\chi_{1519}(22, \cdot)\) None 0 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1519))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1519)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(217))\)\(^{\oplus 2}\)