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Properties

Label 2835.1
Level 2835
Weight 1
Dimension 84
Nonzero newspaces 6
Newform subspaces 12
Sturm bound 559872
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2835 = 3^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 12 \)
Sturm bound: \(559872\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2835))\).

Total New Old
Modular forms 5426 1764 3662
Cusp forms 242 84 158
Eisenstein series 5184 1680 3504

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 52 0 32 0

Trace form

\( 84 q + 8 q^{4} + 4 q^{7} + O(q^{10}) \) \( 84 q + 8 q^{4} + 4 q^{7} + 8 q^{10} + 6 q^{11} - 8 q^{16} - 8 q^{22} + 4 q^{25} - 4 q^{31} + 16 q^{34} + 6 q^{35} - 16 q^{46} + 12 q^{49} + 4 q^{61} - 18 q^{64} + 24 q^{65} + 8 q^{67} - 14 q^{79} - 26 q^{85} + 8 q^{88} - 36 q^{91} + 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2835))\)

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
2835.1.c \(\chi_{2835}(2591, \cdot)\) None 0 1
2835.1.e \(\chi_{2835}(244, \cdot)\) 2835.1.e.a 1 1
2835.1.e.b 1
2835.1.e.c 1
2835.1.e.d 1
2835.1.f \(\chi_{2835}(2024, \cdot)\) None 0 1
2835.1.h \(\chi_{2835}(811, \cdot)\) None 0 1
2835.1.n \(\chi_{2835}(1133, \cdot)\) None 0 2
2835.1.o \(\chi_{2835}(568, \cdot)\) None 0 2
2835.1.q \(\chi_{2835}(2404, \cdot)\) None 0 2
2835.1.s \(\chi_{2835}(296, \cdot)\) None 0 2
2835.1.v \(\chi_{2835}(674, \cdot)\) 2835.1.v.a 8 2
2835.1.w \(\chi_{2835}(1216, \cdot)\) None 0 2
2835.1.x \(\chi_{2835}(1756, \cdot)\) None 0 2
2835.1.y \(\chi_{2835}(809, \cdot)\) None 0 2
2835.1.ba \(\chi_{2835}(134, \cdot)\) None 0 2
2835.1.bc \(\chi_{2835}(1081, \cdot)\) None 0 2
2835.1.bd \(\chi_{2835}(1241, \cdot)\) None 0 2
2835.1.bg \(\chi_{2835}(1189, \cdot)\) None 0 2
2835.1.bi \(\chi_{2835}(649, \cdot)\) None 0 2
2835.1.bk \(\chi_{2835}(701, \cdot)\) None 0 2
2835.1.bm \(\chi_{2835}(1376, \cdot)\) None 0 2
2835.1.bn \(\chi_{2835}(514, \cdot)\) None 0 2
2835.1.bp \(\chi_{2835}(136, \cdot)\) None 0 2
2835.1.br \(\chi_{2835}(2564, \cdot)\) 2835.1.br.a 8 2
2835.1.bw \(\chi_{2835}(298, \cdot)\) None 0 4
2835.1.bx \(\chi_{2835}(782, \cdot)\) None 0 4
2835.1.bz \(\chi_{2835}(458, \cdot)\) None 0 4
2835.1.cb \(\chi_{2835}(757, \cdot)\) None 0 4
2835.1.cd \(\chi_{2835}(163, \cdot)\) None 0 4
2835.1.cg \(\chi_{2835}(647, \cdot)\) None 0 4
2835.1.ci \(\chi_{2835}(188, \cdot)\) 2835.1.ci.a 8 4
2835.1.ci.b 8
2835.1.ck \(\chi_{2835}(1108, \cdot)\) None 0 4
2835.1.cm \(\chi_{2835}(451, \cdot)\) None 0 6
2835.1.cn \(\chi_{2835}(449, \cdot)\) None 0 6
2835.1.co \(\chi_{2835}(179, \cdot)\) None 0 6
2835.1.cp \(\chi_{2835}(181, \cdot)\) None 0 6
2835.1.cr \(\chi_{2835}(586, \cdot)\) None 0 6
2835.1.ct \(\chi_{2835}(44, \cdot)\) None 0 6
2835.1.cv \(\chi_{2835}(116, \cdot)\) None 0 6
2835.1.cw \(\chi_{2835}(559, \cdot)\) 2835.1.cw.a 6 6
2835.1.cw.b 6
2835.1.cy \(\chi_{2835}(19, \cdot)\) None 0 6
2835.1.da \(\chi_{2835}(71, \cdot)\) None 0 6
2835.1.dc \(\chi_{2835}(746, \cdot)\) None 0 6
2835.1.df \(\chi_{2835}(334, \cdot)\) None 0 6
2835.1.dj \(\chi_{2835}(37, \cdot)\) None 0 12
2835.1.dm \(\chi_{2835}(17, \cdot)\) None 0 12
2835.1.do \(\chi_{2835}(62, \cdot)\) None 0 12
2835.1.dq \(\chi_{2835}(172, \cdot)\) None 0 12
2835.1.ds \(\chi_{2835}(127, \cdot)\) None 0 12
2835.1.dt \(\chi_{2835}(143, \cdot)\) None 0 12
2835.1.dv \(\chi_{2835}(229, \cdot)\) None 0 18
2835.1.dw \(\chi_{2835}(11, \cdot)\) None 0 18
2835.1.dx \(\chi_{2835}(166, \cdot)\) None 0 18
2835.1.dy \(\chi_{2835}(74, \cdot)\) None 0 18
2835.1.ef \(\chi_{2835}(76, \cdot)\) None 0 18
2835.1.eg \(\chi_{2835}(29, \cdot)\) None 0 18
2835.1.eh \(\chi_{2835}(31, \cdot)\) None 0 18
2835.1.ei \(\chi_{2835}(254, \cdot)\) None 0 18
2835.1.ej \(\chi_{2835}(94, \cdot)\) None 0 18
2835.1.ek \(\chi_{2835}(191, \cdot)\) None 0 18
2835.1.el \(\chi_{2835}(34, \cdot)\) 2835.1.el.a 18 18
2835.1.el.b 18
2835.1.em \(\chi_{2835}(176, \cdot)\) None 0 18
2835.1.es \(\chi_{2835}(47, \cdot)\) None 0 36
2835.1.et \(\chi_{2835}(83, \cdot)\) None 0 36
2835.1.eu \(\chi_{2835}(22, \cdot)\) None 0 36
2835.1.ev \(\chi_{2835}(67, \cdot)\) None 0 36
2835.1.fa \(\chi_{2835}(38, \cdot)\) None 0 36
2835.1.fb \(\chi_{2835}(58, \cdot)\) None 0 36

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2835))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2835)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(567))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(945))\)\(^{\oplus 2}\)