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Properties

Label 2016.1
Level 2016
Weight 1
Dimension 71
Nonzero newspaces 12
Newform subspaces 20
Sturm bound 221184
Trace bound 25

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Defining parameters

Level: \( N \) = \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 20 \)
Sturm bound: \(221184\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2016))\).

Total New Old
Modular forms 3524 521 3003
Cusp forms 452 71 381
Eisenstein series 3072 450 2622

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 51 20 0 0

Trace form

\( 71 q + 2 q^{3} + 2 q^{5} + q^{7} + O(q^{10}) \) \( 71 q + 2 q^{3} + 2 q^{5} + q^{7} + 2 q^{11} - 4 q^{13} - 8 q^{15} + 4 q^{16} + 10 q^{17} + 4 q^{19} - 2 q^{21} - 4 q^{22} + 2 q^{23} - 13 q^{25} + 8 q^{27} - 4 q^{29} - 6 q^{31} - 4 q^{33} + 4 q^{35} + 6 q^{37} + 4 q^{39} + 8 q^{41} - 4 q^{44} - 19 q^{49} - 2 q^{51} - 2 q^{53} - 4 q^{56} - 4 q^{57} + 4 q^{61} + 4 q^{63} + 2 q^{65} + 4 q^{67} - 16 q^{69} - 2 q^{71} + 2 q^{73} - 4 q^{74} + 2 q^{77} + 8 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{85} - 2 q^{89} + 4 q^{91} + 4 q^{92} + 4 q^{93} + 8 q^{95} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2016))\)

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
2016.1.d \(\chi_{2016}(449, \cdot)\) None 0 1
2016.1.e \(\chi_{2016}(1007, \cdot)\) 2016.1.e.a 4 1
2016.1.f \(\chi_{2016}(1441, \cdot)\) 2016.1.f.a 4 1
2016.1.g \(\chi_{2016}(1135, \cdot)\) None 0 1
2016.1.l \(\chi_{2016}(433, \cdot)\) 2016.1.l.a 1 1
2016.1.l.b 2
2016.1.m \(\chi_{2016}(127, \cdot)\) None 0 1
2016.1.n \(\chi_{2016}(1457, \cdot)\) None 0 1
2016.1.o \(\chi_{2016}(2015, \cdot)\) None 0 1
2016.1.u \(\chi_{2016}(937, \cdot)\) None 0 2
2016.1.w \(\chi_{2016}(953, \cdot)\) None 0 2
2016.1.y \(\chi_{2016}(503, \cdot)\) None 0 2
2016.1.ba \(\chi_{2016}(631, \cdot)\) None 0 2
2016.1.bc \(\chi_{2016}(47, \cdot)\) None 0 2
2016.1.bd \(\chi_{2016}(65, \cdot)\) None 0 2
2016.1.bi \(\chi_{2016}(79, \cdot)\) 2016.1.bi.a 4 2
2016.1.bj \(\chi_{2016}(1825, \cdot)\) None 0 2
2016.1.bk \(\chi_{2016}(1151, \cdot)\) None 0 2
2016.1.bl \(\chi_{2016}(305, \cdot)\) None 0 2
2016.1.bo \(\chi_{2016}(113, \cdot)\) None 0 2
2016.1.bp \(\chi_{2016}(383, \cdot)\) None 0 2
2016.1.bq \(\chi_{2016}(401, \cdot)\) None 0 2
2016.1.br \(\chi_{2016}(671, \cdot)\) None 0 2
2016.1.bv \(\chi_{2016}(1105, \cdot)\) 2016.1.bv.a 2 2
2016.1.bv.b 2
2016.1.bv.c 4
2016.1.bw \(\chi_{2016}(1663, \cdot)\) 2016.1.bw.a 4 2
2016.1.bx \(\chi_{2016}(241, \cdot)\) None 0 2
2016.1.by \(\chi_{2016}(799, \cdot)\) None 0 2
2016.1.cd \(\chi_{2016}(415, \cdot)\) 2016.1.cd.a 4 2
2016.1.ce \(\chi_{2016}(145, \cdot)\) 2016.1.ce.a 4 2
2016.1.cf \(\chi_{2016}(1423, \cdot)\) None 0 2
2016.1.cg \(\chi_{2016}(577, \cdot)\) None 0 2
2016.1.cl \(\chi_{2016}(97, \cdot)\) None 0 2
2016.1.cm \(\chi_{2016}(655, \cdot)\) 2016.1.cm.a 4 2
2016.1.cn \(\chi_{2016}(481, \cdot)\) None 0 2
2016.1.co \(\chi_{2016}(463, \cdot)\) None 0 2
2016.1.ct \(\chi_{2016}(1121, \cdot)\) None 0 2
2016.1.cu \(\chi_{2016}(1391, \cdot)\) None 0 2
2016.1.cv \(\chi_{2016}(641, \cdot)\) None 0 2
2016.1.cw \(\chi_{2016}(335, \cdot)\) None 0 2
2016.1.db \(\chi_{2016}(143, \cdot)\) None 0 2
2016.1.dc \(\chi_{2016}(737, \cdot)\) None 0 2
2016.1.dd \(\chi_{2016}(319, \cdot)\) 2016.1.dd.a 4 2
2016.1.de \(\chi_{2016}(817, \cdot)\) None 0 2
2016.1.di \(\chi_{2016}(1055, \cdot)\) None 0 2
2016.1.dj \(\chi_{2016}(977, \cdot)\) None 0 2
2016.1.dl \(\chi_{2016}(379, \cdot)\) None 0 4
2016.1.dn \(\chi_{2016}(251, \cdot)\) 2016.1.dn.a 4 4
2016.1.dn.b 4
2016.1.dn.c 4
2016.1.dn.d 4
2016.1.dp \(\chi_{2016}(181, \cdot)\) 2016.1.dp.a 4 4
2016.1.dp.b 4
2016.1.dp.c 4
2016.1.dr \(\chi_{2016}(197, \cdot)\) None 0 4
2016.1.dt \(\chi_{2016}(281, \cdot)\) None 0 4
2016.1.dv \(\chi_{2016}(265, \cdot)\) None 0 4
2016.1.dx \(\chi_{2016}(311, \cdot)\) None 0 4
2016.1.dy \(\chi_{2016}(151, \cdot)\) None 0 4
2016.1.eb \(\chi_{2016}(487, \cdot)\) None 0 4
2016.1.ed \(\chi_{2016}(215, \cdot)\) None 0 4
2016.1.ee \(\chi_{2016}(887, \cdot)\) None 0 4
2016.1.eh \(\chi_{2016}(583, \cdot)\) None 0 4
2016.1.ej \(\chi_{2016}(313, \cdot)\) None 0 4
2016.1.el \(\chi_{2016}(233, \cdot)\) None 0 4
2016.1.em \(\chi_{2016}(137, \cdot)\) None 0 4
2016.1.eo \(\chi_{2016}(745, \cdot)\) None 0 4
2016.1.er \(\chi_{2016}(73, \cdot)\) None 0 4
2016.1.et \(\chi_{2016}(473, \cdot)\) None 0 4
2016.1.ev \(\chi_{2016}(295, \cdot)\) None 0 4
2016.1.ex \(\chi_{2016}(167, \cdot)\) None 0 4
2016.1.ey \(\chi_{2016}(83, \cdot)\) None 0 8
2016.1.fa \(\chi_{2016}(43, \cdot)\) None 0 8
2016.1.fd \(\chi_{2016}(229, \cdot)\) None 0 8
2016.1.fe \(\chi_{2016}(221, \cdot)\) None 0 8
2016.1.ff \(\chi_{2016}(53, \cdot)\) None 0 8
2016.1.fi \(\chi_{2016}(325, \cdot)\) None 0 8
2016.1.fj \(\chi_{2016}(61, \cdot)\) None 0 8
2016.1.fn \(\chi_{2016}(149, \cdot)\) None 0 8
2016.1.fp \(\chi_{2016}(403, \cdot)\) None 0 8
2016.1.fq \(\chi_{2016}(395, \cdot)\) None 0 8
2016.1.fr \(\chi_{2016}(59, \cdot)\) None 0 8
2016.1.fu \(\chi_{2016}(67, \cdot)\) None 0 8
2016.1.fv \(\chi_{2016}(163, \cdot)\) None 0 8
2016.1.fz \(\chi_{2016}(131, \cdot)\) None 0 8
2016.1.ga \(\chi_{2016}(29, \cdot)\) None 0 8
2016.1.gc \(\chi_{2016}(13, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2016))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2016)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(672))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1008))\)\(^{\oplus 2}\)