Properties

Label 855.1
Level 855
Weight 1
Dimension 61
Nonzero newspaces 7
Newform subspaces 13
Sturm bound 51840
Trace bound 10

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Defining parameters

Level: \( N \) = \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 13 \)
Sturm bound: \(51840\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(855))\).

Total New Old
Modular forms 1276 519 757
Cusp forms 124 61 63
Eisenstein series 1152 458 694

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 45 0 16 0

Trace form

\( 61 q - 11 q^{4} + q^{5} + O(q^{10}) \) \( 61 q - 11 q^{4} + q^{5} + 2 q^{11} - 4 q^{13} - 35 q^{16} - 9 q^{19} + 3 q^{20} + 4 q^{22} - 8 q^{24} - 5 q^{25} - 20 q^{26} + 16 q^{30} - 16 q^{31} + 8 q^{34} - 8 q^{36} - 8 q^{37} + 12 q^{43} + 30 q^{44} - 5 q^{49} - 8 q^{54} - 10 q^{55} + 2 q^{61} - 13 q^{64} + 16 q^{66} - 4 q^{70} - 8 q^{73} + 4 q^{74} + q^{76} + 4 q^{79} - 19 q^{80} - 4 q^{82} - 10 q^{85} - 8 q^{88} + 4 q^{91} - 11 q^{95} + 8 q^{96} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(855))\)

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
855.1.d \(\chi_{855}(476, \cdot)\) None 0 1
855.1.e \(\chi_{855}(721, \cdot)\) None 0 1
855.1.f \(\chi_{855}(134, \cdot)\) None 0 1
855.1.g \(\chi_{855}(379, \cdot)\) 855.1.g.a 1 1
855.1.g.b 2
855.1.g.c 2
855.1.m \(\chi_{855}(512, \cdot)\) 855.1.m.a 4 2
855.1.m.b 4
855.1.o \(\chi_{855}(172, \cdot)\) None 0 2
855.1.q \(\chi_{855}(601, \cdot)\) None 0 2
855.1.r \(\chi_{855}(581, \cdot)\) None 0 2
855.1.u \(\chi_{855}(539, \cdot)\) 855.1.u.a 8 2
855.1.v \(\chi_{855}(559, \cdot)\) 855.1.v.a 4 2
855.1.y \(\chi_{855}(544, \cdot)\) None 0 2
855.1.z \(\chi_{855}(94, \cdot)\) 855.1.z.a 2 2
855.1.z.b 2
855.1.z.c 4
855.1.z.d 8
855.1.ba \(\chi_{855}(524, \cdot)\) None 0 2
855.1.bb \(\chi_{855}(419, \cdot)\) None 0 2
855.1.bf \(\chi_{855}(31, \cdot)\) None 0 2
855.1.bg \(\chi_{855}(151, \cdot)\) None 0 2
855.1.bh \(\chi_{855}(11, \cdot)\) None 0 2
855.1.bi \(\chi_{855}(191, \cdot)\) None 0 2
855.1.bn \(\chi_{855}(26, \cdot)\) None 0 2
855.1.bo \(\chi_{855}(46, \cdot)\) None 0 2
855.1.bq \(\chi_{855}(259, \cdot)\) None 0 2
855.1.br \(\chi_{855}(239, \cdot)\) None 0 2
855.1.bw \(\chi_{855}(7, \cdot)\) None 0 4
855.1.by \(\chi_{855}(122, \cdot)\) None 0 4
855.1.ca \(\chi_{855}(8, \cdot)\) None 0 4
855.1.cb \(\chi_{855}(277, \cdot)\) None 0 4
855.1.cd \(\chi_{855}(58, \cdot)\) None 0 4
855.1.cf \(\chi_{855}(392, \cdot)\) None 0 4
855.1.ch \(\chi_{855}(113, \cdot)\) None 0 4
855.1.ck \(\chi_{855}(163, \cdot)\) 855.1.ck.a 8 4
855.1.cl \(\chi_{855}(79, \cdot)\) None 0 6
855.1.cm \(\chi_{855}(74, \cdot)\) None 0 6
855.1.cr \(\chi_{855}(101, \cdot)\) None 0 6
855.1.cs \(\chi_{855}(91, \cdot)\) None 0 6
855.1.ct \(\chi_{855}(161, \cdot)\) None 0 6
855.1.cu \(\chi_{855}(166, \cdot)\) None 0 6
855.1.cv \(\chi_{855}(149, \cdot)\) None 0 6
855.1.cw \(\chi_{855}(109, \cdot)\) 855.1.cw.a 12 6
855.1.cx \(\chi_{855}(44, \cdot)\) None 0 6
855.1.cy \(\chi_{855}(34, \cdot)\) None 0 6
855.1.de \(\chi_{855}(421, \cdot)\) None 0 6
855.1.df \(\chi_{855}(416, \cdot)\) None 0 6
855.1.dg \(\chi_{855}(212, \cdot)\) None 0 12
855.1.di \(\chi_{855}(43, \cdot)\) None 0 12
855.1.dj \(\chi_{855}(28, \cdot)\) None 0 12
855.1.do \(\chi_{855}(2, \cdot)\) None 0 12
855.1.dp \(\chi_{855}(53, \cdot)\) None 0 12
855.1.dr \(\chi_{855}(112, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(855))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(855)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 2}\)