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Properties

Label 2176.1
Level 2176
Weight 1
Dimension 66
Nonzero newspaces 4
Newform subspaces 18
Sturm bound 294912
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2176 = 2^{7} \cdot 17 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 18 \)
Sturm bound: \(294912\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2176))\).

Total New Old
Modular forms 2824 786 2038
Cusp forms 264 66 198
Eisenstein series 2560 720 1840

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 66 0 0 0

Trace form

\( 66 q + 2 q^{9} + O(q^{10}) \) \( 66 q + 2 q^{9} + 2 q^{17} - 10 q^{25} + 8 q^{33} - 8 q^{41} + 6 q^{49} + 8 q^{73} - 6 q^{81} + 4 q^{89} + 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2176))\)

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
2176.1.d \(\chi_{2176}(511, \cdot)\) None 0 1
2176.1.e \(\chi_{2176}(1087, \cdot)\) 2176.1.e.a 1 1
2176.1.e.b 1
2176.1.e.c 1
2176.1.e.d 1
2176.1.e.e 2
2176.1.e.f 4
2176.1.f \(\chi_{2176}(1599, \cdot)\) None 0 1
2176.1.g \(\chi_{2176}(2175, \cdot)\) None 0 1
2176.1.i \(\chi_{2176}(735, \cdot)\) None 0 2
2176.1.k \(\chi_{2176}(543, \cdot)\) None 0 2
2176.1.n \(\chi_{2176}(191, \cdot)\) 2176.1.n.a 2 2
2176.1.n.b 2
2176.1.n.c 2
2176.1.n.d 2
2176.1.p \(\chi_{2176}(1279, \cdot)\) None 0 2
2176.1.q \(\chi_{2176}(1055, \cdot)\) None 0 2
2176.1.t \(\chi_{2176}(863, \cdot)\) None 0 2
2176.1.u \(\chi_{2176}(399, \cdot)\) None 0 4
2176.1.w \(\chi_{2176}(111, \cdot)\) None 0 4
2176.1.y \(\chi_{2176}(591, \cdot)\) None 0 4
2176.1.ba \(\chi_{2176}(127, \cdot)\) None 0 4
2176.1.bf \(\chi_{2176}(287, \cdot)\) None 0 4
2176.1.bh \(\chi_{2176}(223, \cdot)\) None 0 4
2176.1.bi \(\chi_{2176}(239, \cdot)\) None 0 4
2176.1.bj \(\chi_{2176}(271, \cdot)\) None 0 4
2176.1.bl \(\chi_{2176}(831, \cdot)\) 2176.1.bl.a 4 4
2176.1.bl.b 4
2176.1.bl.c 4
2176.1.bl.d 4
2176.1.bm \(\chi_{2176}(47, \cdot)\) None 0 4
2176.1.bo \(\chi_{2176}(15, \cdot)\) None 0 4
2176.1.br \(\chi_{2176}(495, \cdot)\) None 0 4
2176.1.bt \(\chi_{2176}(41, \cdot)\) None 0 8
2176.1.bu \(\chi_{2176}(57, \cdot)\) None 0 8
2176.1.bw \(\chi_{2176}(87, \cdot)\) None 0 8
2176.1.bz \(\chi_{2176}(265, \cdot)\) None 0 8
2176.1.cb \(\chi_{2176}(505, \cdot)\) None 0 8
2176.1.cc \(\chi_{2176}(737, \cdot)\) None 0 8
2176.1.ch \(\chi_{2176}(337, \cdot)\) None 0 8
2176.1.ci \(\chi_{2176}(73, \cdot)\) None 0 8
2176.1.ck \(\chi_{2176}(105, \cdot)\) None 0 8
2176.1.cm \(\chi_{2176}(135, \cdot)\) None 0 8
2176.1.co \(\chi_{2176}(65, \cdot)\) 2176.1.co.a 8 8
2176.1.co.b 8
2176.1.co.c 8
2176.1.co.d 8
2176.1.cq \(\chi_{2176}(241, \cdot)\) None 0 8
2176.1.ct \(\chi_{2176}(55, \cdot)\) None 0 8
2176.1.cu \(\chi_{2176}(183, \cdot)\) None 0 8
2176.1.cw \(\chi_{2176}(369, \cdot)\) None 0 8
2176.1.cz \(\chi_{2176}(129, \cdot)\) None 0 8
2176.1.db \(\chi_{2176}(103, \cdot)\) None 0 8
2176.1.dd \(\chi_{2176}(113, \cdot)\) None 0 8
2176.1.de \(\chi_{2176}(359, \cdot)\) None 0 8
2176.1.df \(\chi_{2176}(247, \cdot)\) None 0 8
2176.1.dg \(\chi_{2176}(97, \cdot)\) None 0 8
2176.1.di \(\chi_{2176}(151, \cdot)\) None 0 8
2176.1.dk \(\chi_{2176}(537, \cdot)\) None 0 8
2176.1.dn \(\chi_{2176}(329, \cdot)\) None 0 8
2176.1.do \(\chi_{2176}(37, \cdot)\) None 0 16
2176.1.dt \(\chi_{2176}(245, \cdot)\) None 0 16
2176.1.dv \(\chi_{2176}(115, \cdot)\) None 0 16
2176.1.dx \(\chi_{2176}(197, \cdot)\) None 0 16
2176.1.dz \(\chi_{2176}(67, \cdot)\) None 0 16
2176.1.ea \(\chi_{2176}(43, \cdot)\) None 0 16
2176.1.ec \(\chi_{2176}(219, \cdot)\) None 0 16
2176.1.ed \(\chi_{2176}(155, \cdot)\) None 0 16
2176.1.eh \(\chi_{2176}(19, \cdot)\) None 0 16
2176.1.ei \(\chi_{2176}(35, \cdot)\) None 0 16
2176.1.ek \(\chi_{2176}(141, \cdot)\) None 0 16
2176.1.em \(\chi_{2176}(251, \cdot)\) None 0 16
2176.1.eo \(\chi_{2176}(29, \cdot)\) None 0 16
2176.1.eq \(\chi_{2176}(5, \cdot)\) None 0 16
2176.1.er \(\chi_{2176}(109, \cdot)\) None 0 16
2176.1.es \(\chi_{2176}(45, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2176))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2176)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 14}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(544))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1088))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2176))\)\(^{\oplus 1}\)