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Properties

Label 1008.1
Level 1008
Weight 1
Dimension 49
Nonzero newspaces 10
Newform subspaces 14
Sturm bound 55296
Trace bound 10

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Defining parameters

Level: \( N \) = \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 14 \)
Sturm bound: \(55296\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1008))\).

Total New Old
Modular forms 1544 252 1292
Cusp forms 200 49 151
Eisenstein series 1344 203 1141

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 21 8 20 0

Trace form

\( 49 q + 2 q^{4} - 2 q^{5} - 6 q^{7} - 2 q^{9} + O(q^{10}) \) \( 49 q + 2 q^{4} - 2 q^{5} - 6 q^{7} - 2 q^{9} + 4 q^{10} + 2 q^{11} + 12 q^{13} + 2 q^{14} + 6 q^{16} - 4 q^{17} + 5 q^{19} - 8 q^{21} + 14 q^{22} + 4 q^{25} - 4 q^{28} + 6 q^{29} - 3 q^{31} - 4 q^{33} - 8 q^{34} - q^{37} - 4 q^{40} - 4 q^{41} - 6 q^{43} - 2 q^{44} - 4 q^{45} + 4 q^{46} - 4 q^{49} + 2 q^{50} - 4 q^{52} + 2 q^{53} - 2 q^{56} + 4 q^{57} - 10 q^{58} - 8 q^{61} + 2 q^{64} + 2 q^{65} - 7 q^{67} - 4 q^{69} - 5 q^{73} - 2 q^{74} - 8 q^{76} - 6 q^{77} - 5 q^{79} + 2 q^{81} - 4 q^{85} + 2 q^{86} - 14 q^{88} - 4 q^{89} - 5 q^{91} - 4 q^{94} + 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1008))\)

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
1008.1.d \(\chi_{1008}(449, \cdot)\) None 0 1
1008.1.e \(\chi_{1008}(503, \cdot)\) None 0 1
1008.1.f \(\chi_{1008}(433, \cdot)\) 1008.1.f.a 1 1
1008.1.g \(\chi_{1008}(631, \cdot)\) None 0 1
1008.1.l \(\chi_{1008}(937, \cdot)\) None 0 1
1008.1.m \(\chi_{1008}(127, \cdot)\) None 0 1
1008.1.n \(\chi_{1008}(953, \cdot)\) None 0 1
1008.1.o \(\chi_{1008}(1007, \cdot)\) None 0 1
1008.1.u \(\chi_{1008}(181, \cdot)\) 1008.1.u.a 2 2
1008.1.u.b 2
1008.1.u.c 2
1008.1.w \(\chi_{1008}(197, \cdot)\) None 0 2
1008.1.y \(\chi_{1008}(251, \cdot)\) 1008.1.y.a 4 2
1008.1.y.b 4
1008.1.ba \(\chi_{1008}(379, \cdot)\) None 0 2
1008.1.bc \(\chi_{1008}(311, \cdot)\) None 0 2
1008.1.bd \(\chi_{1008}(65, \cdot)\) None 0 2
1008.1.bi \(\chi_{1008}(583, \cdot)\) None 0 2
1008.1.bj \(\chi_{1008}(817, \cdot)\) None 0 2
1008.1.bk \(\chi_{1008}(143, \cdot)\) None 0 2
1008.1.bl \(\chi_{1008}(233, \cdot)\) None 0 2
1008.1.bo \(\chi_{1008}(281, \cdot)\) None 0 2
1008.1.bp \(\chi_{1008}(383, \cdot)\) None 0 2
1008.1.bq \(\chi_{1008}(137, \cdot)\) None 0 2
1008.1.br \(\chi_{1008}(335, \cdot)\) None 0 2
1008.1.bv \(\chi_{1008}(265, \cdot)\) None 0 2
1008.1.bw \(\chi_{1008}(655, \cdot)\) 1008.1.bw.a 4 2
1008.1.bx \(\chi_{1008}(745, \cdot)\) None 0 2
1008.1.by \(\chi_{1008}(463, \cdot)\) None 0 2
1008.1.cd \(\chi_{1008}(415, \cdot)\) 1008.1.cd.a 2 2
1008.1.cd.b 2
1008.1.ce \(\chi_{1008}(73, \cdot)\) None 0 2
1008.1.cf \(\chi_{1008}(487, \cdot)\) None 0 2
1008.1.cg \(\chi_{1008}(145, \cdot)\) 1008.1.cg.a 2 2
1008.1.cl \(\chi_{1008}(97, \cdot)\) None 0 2
1008.1.cm \(\chi_{1008}(151, \cdot)\) None 0 2
1008.1.cn \(\chi_{1008}(241, \cdot)\) None 0 2
1008.1.co \(\chi_{1008}(295, \cdot)\) None 0 2
1008.1.ct \(\chi_{1008}(113, \cdot)\) None 0 2
1008.1.cu \(\chi_{1008}(887, \cdot)\) None 0 2
1008.1.cv \(\chi_{1008}(401, \cdot)\) None 0 2
1008.1.cw \(\chi_{1008}(167, \cdot)\) None 0 2
1008.1.db \(\chi_{1008}(215, \cdot)\) None 0 2
1008.1.dc \(\chi_{1008}(305, \cdot)\) 1008.1.dc.a 4 2
1008.1.dd \(\chi_{1008}(79, \cdot)\) 1008.1.dd.a 4 2
1008.1.de \(\chi_{1008}(313, \cdot)\) None 0 2
1008.1.di \(\chi_{1008}(47, \cdot)\) None 0 2
1008.1.dj \(\chi_{1008}(473, \cdot)\) None 0 2
1008.1.dl \(\chi_{1008}(29, \cdot)\) None 0 4
1008.1.dn \(\chi_{1008}(13, \cdot)\) None 0 4
1008.1.dp \(\chi_{1008}(59, \cdot)\) None 0 4
1008.1.dq \(\chi_{1008}(403, \cdot)\) None 0 4
1008.1.dt \(\chi_{1008}(163, \cdot)\) 1008.1.dt.a 8 4
1008.1.dv \(\chi_{1008}(395, \cdot)\) None 0 4
1008.1.dw \(\chi_{1008}(131, \cdot)\) None 0 4
1008.1.dz \(\chi_{1008}(67, \cdot)\) None 0 4
1008.1.eb \(\chi_{1008}(61, \cdot)\) None 0 4
1008.1.ed \(\chi_{1008}(53, \cdot)\) 1008.1.ed.a 8 4
1008.1.ee \(\chi_{1008}(149, \cdot)\) None 0 4
1008.1.eg \(\chi_{1008}(229, \cdot)\) None 0 4
1008.1.ej \(\chi_{1008}(325, \cdot)\) None 0 4
1008.1.el \(\chi_{1008}(221, \cdot)\) None 0 4
1008.1.en \(\chi_{1008}(43, \cdot)\) None 0 4
1008.1.ep \(\chi_{1008}(83, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1008))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1008)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 2}\)