Properties

Label 775.1
Level 775
Weight 1
Dimension 30
Nonzero newspaces 4
Newform subspaces 8
Sturm bound 48000
Trace bound 4

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Defining parameters

Level: \( N \) = \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 8 \)
Sturm bound: \(48000\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(775))\).

Total New Old
Modular forms 879 625 254
Cusp forms 39 30 9
Eisenstein series 840 595 245

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 30 0 0 0

Trace form

\( 30 q + q^{2} + 3 q^{4} + q^{7} - 7 q^{8} + 2 q^{9} + O(q^{10}) \) \( 30 q + q^{2} + 3 q^{4} + q^{7} - 7 q^{8} + 2 q^{9} - 19 q^{14} - 6 q^{16} + q^{18} + q^{19} - 6 q^{28} - 6 q^{32} - 6 q^{35} - 3 q^{36} + 23 q^{38} - 6 q^{40} - 3 q^{41} - 8 q^{47} + 3 q^{49} - 9 q^{56} + q^{59} + q^{62} + q^{63} + 14 q^{64} - 8 q^{67} - 6 q^{70} - 3 q^{71} - 7 q^{72} - 6 q^{76} - 6 q^{80} - 7 q^{82} + 24 q^{90} + 2 q^{94} - 6 q^{95} + q^{97} - 6 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(775))\)

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
775.1.c \(\chi_{775}(774, \cdot)\) 775.1.c.a 2 1
775.1.d \(\chi_{775}(526, \cdot)\) 775.1.d.a 1 1
775.1.d.b 1
775.1.d.c 2
775.1.g \(\chi_{775}(32, \cdot)\) None 0 2
775.1.n \(\chi_{775}(99, \cdot)\) None 0 2
775.1.p \(\chi_{775}(26, \cdot)\) None 0 2
775.1.q \(\chi_{775}(339, \cdot)\) None 0 4
775.1.s \(\chi_{775}(246, \cdot)\) None 0 4
775.1.t \(\chi_{775}(151, \cdot)\) None 0 4
775.1.u \(\chi_{775}(91, \cdot)\) None 0 4
775.1.v \(\chi_{775}(46, \cdot)\) None 0 4
775.1.w \(\chi_{775}(61, \cdot)\) 775.1.w.a 4 4
775.1.w.b 8
775.1.y \(\chi_{775}(399, \cdot)\) None 0 4
775.1.z \(\chi_{775}(154, \cdot)\) 775.1.z.a 4 4
775.1.z.b 8
775.1.ba \(\chi_{775}(89, \cdot)\) None 0 4
775.1.bb \(\chi_{775}(54, \cdot)\) None 0 4
775.1.bg \(\chi_{775}(29, \cdot)\) None 0 4
775.1.bh \(\chi_{775}(581, \cdot)\) None 0 4
775.1.bi \(\chi_{775}(118, \cdot)\) None 0 4
775.1.bq \(\chi_{775}(2, \cdot)\) None 0 8
775.1.bt \(\chi_{775}(233, \cdot)\) None 0 8
775.1.bu \(\chi_{775}(33, \cdot)\) None 0 8
775.1.bv \(\chi_{775}(63, \cdot)\) None 0 8
775.1.bw \(\chi_{775}(188, \cdot)\) None 0 8
775.1.cb \(\chi_{775}(132, \cdot)\) None 0 8
775.1.cd \(\chi_{775}(34, \cdot)\) None 0 8
775.1.ce \(\chi_{775}(6, \cdot)\) None 0 8
775.1.cf \(\chi_{775}(11, \cdot)\) None 0 8
775.1.cg \(\chi_{775}(146, \cdot)\) None 0 8
775.1.ch \(\chi_{775}(176, \cdot)\) None 0 8
775.1.ci \(\chi_{775}(21, \cdot)\) None 0 8
775.1.cj \(\chi_{775}(44, \cdot)\) None 0 8
775.1.co \(\chi_{775}(79, \cdot)\) None 0 8
775.1.cp \(\chi_{775}(84, \cdot)\) None 0 8
775.1.cq \(\chi_{775}(119, \cdot)\) None 0 8
775.1.cr \(\chi_{775}(24, \cdot)\) None 0 8
775.1.ct \(\chi_{775}(136, \cdot)\) None 0 8
775.1.cv \(\chi_{775}(133, \cdot)\) None 0 16
775.1.cw \(\chi_{775}(7, \cdot)\) None 0 16
775.1.db \(\chi_{775}(112, \cdot)\) None 0 16
775.1.dc \(\chi_{775}(67, \cdot)\) None 0 16
775.1.dd \(\chi_{775}(28, \cdot)\) None 0 16
775.1.de \(\chi_{775}(38, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(775))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(775)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 2}\)