Properties

Label 2240.1
Level 2240
Weight 1
Dimension 84
Nonzero newspaces 8
Newform subspaces 20
Sturm bound 294912
Trace bound 33

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 20 \)
Sturm bound: \(294912\)
Trace bound: \(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2240))\).

Total New Old
Modular forms 3780 744 3036
Cusp forms 324 84 240
Eisenstein series 3456 660 2796

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 60 0 24 0

Trace form

\( 84q + 4q^{5} - 20q^{9} + O(q^{10}) \) \( 84q + 4q^{5} - 20q^{9} + 4q^{21} - 12q^{25} + 12q^{29} + 4q^{33} - 24q^{41} - 16q^{45} + 24q^{49} + 4q^{53} - 24q^{57} + 4q^{61} - 8q^{65} - 16q^{69} - 4q^{77} - 36q^{81} + 4q^{85} - 8q^{89} + 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2240))\)

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
2240.1.c \(\chi_{2240}(1889, \cdot)\) 2240.1.c.a 2 1
2240.1.c.b 2
2240.1.c.c 4
2240.1.c.d 4
2240.1.d \(\chi_{2240}(1471, \cdot)\) None 0 1
2240.1.f \(\chi_{2240}(321, \cdot)\) None 0 1
2240.1.i \(\chi_{2240}(799, \cdot)\) None 0 1
2240.1.j \(\chi_{2240}(1919, \cdot)\) None 0 1
2240.1.m \(\chi_{2240}(1441, \cdot)\) None 0 1
2240.1.o \(\chi_{2240}(351, \cdot)\) None 0 1
2240.1.p \(\chi_{2240}(769, \cdot)\) 2240.1.p.a 1 1
2240.1.p.b 1
2240.1.p.c 1
2240.1.p.d 1
2240.1.p.e 4
2240.1.s \(\chi_{2240}(1233, \cdot)\) None 0 2
2240.1.u \(\chi_{2240}(1903, \cdot)\) None 0 2
2240.1.v \(\chi_{2240}(447, \cdot)\) None 0 2
2240.1.y \(\chi_{2240}(673, \cdot)\) None 0 2
2240.1.z \(\chi_{2240}(881, \cdot)\) None 0 2
2240.1.ba \(\chi_{2240}(239, \cdot)\) None 0 2
2240.1.bf \(\chi_{2240}(209, \cdot)\) None 0 2
2240.1.bg \(\chi_{2240}(911, \cdot)\) None 0 2
2240.1.bh \(\chi_{2240}(897, \cdot)\) None 0 2
2240.1.bk \(\chi_{2240}(223, \cdot)\) 2240.1.bk.a 8 2
2240.1.bk.b 8
2240.1.bm \(\chi_{2240}(783, \cdot)\) None 0 2
2240.1.bo \(\chi_{2240}(113, \cdot)\) None 0 2
2240.1.bp \(\chi_{2240}(991, \cdot)\) None 0 2
2240.1.br \(\chi_{2240}(129, \cdot)\) 2240.1.br.a 8 2
2240.1.bt \(\chi_{2240}(319, \cdot)\) 2240.1.bt.a 2 2
2240.1.bt.b 2
2240.1.bt.c 4
2240.1.bu \(\chi_{2240}(481, \cdot)\) None 0 2
2240.1.bx \(\chi_{2240}(1601, \cdot)\) None 0 2
2240.1.by \(\chi_{2240}(1439, \cdot)\) None 0 2
2240.1.ca \(\chi_{2240}(929, \cdot)\) 2240.1.ca.a 4 2
2240.1.ca.b 4
2240.1.cd \(\chi_{2240}(191, \cdot)\) None 0 2
2240.1.ce \(\chi_{2240}(489, \cdot)\) None 0 4
2240.1.cf \(\chi_{2240}(71, \cdot)\) None 0 4
2240.1.ck \(\chi_{2240}(57, \cdot)\) None 0 4
2240.1.cl \(\chi_{2240}(727, \cdot)\) None 0 4
2240.1.co \(\chi_{2240}(167, \cdot)\) None 0 4
2240.1.cp \(\chi_{2240}(617, \cdot)\) None 0 4
2240.1.cq \(\chi_{2240}(519, \cdot)\) None 0 4
2240.1.cr \(\chi_{2240}(41, \cdot)\) None 0 4
2240.1.cu \(\chi_{2240}(47, \cdot)\) None 0 4
2240.1.cw \(\chi_{2240}(753, \cdot)\) None 0 4
2240.1.cz \(\chi_{2240}(607, \cdot)\) None 0 4
2240.1.da \(\chi_{2240}(193, \cdot)\) 2240.1.da.a 8 4
2240.1.dc \(\chi_{2240}(431, \cdot)\) None 0 4
2240.1.dd \(\chi_{2240}(369, \cdot)\) None 0 4
2240.1.di \(\chi_{2240}(79, \cdot)\) None 0 4
2240.1.dj \(\chi_{2240}(241, \cdot)\) None 0 4
2240.1.dl \(\chi_{2240}(417, \cdot)\) 2240.1.dl.a 8 4
2240.1.dl.b 8
2240.1.dm \(\chi_{2240}(383, \cdot)\) None 0 4
2240.1.do \(\chi_{2240}(177, \cdot)\) None 0 4
2240.1.dq \(\chi_{2240}(943, \cdot)\) None 0 4
2240.1.ds \(\chi_{2240}(477, \cdot)\) None 0 8
2240.1.dt \(\chi_{2240}(27, \cdot)\) None 0 8
2240.1.ea \(\chi_{2240}(69, \cdot)\) None 0 8
2240.1.eb \(\chi_{2240}(211, \cdot)\) None 0 8
2240.1.ec \(\chi_{2240}(181, \cdot)\) None 0 8
2240.1.ed \(\chi_{2240}(99, \cdot)\) None 0 8
2240.1.ee \(\chi_{2240}(307, \cdot)\) None 0 8
2240.1.ef \(\chi_{2240}(197, \cdot)\) None 0 8
2240.1.ek \(\chi_{2240}(201, \cdot)\) None 0 8
2240.1.el \(\chi_{2240}(39, \cdot)\) None 0 8
2240.1.em \(\chi_{2240}(327, \cdot)\) None 0 8
2240.1.en \(\chi_{2240}(137, \cdot)\) None 0 8
2240.1.eq \(\chi_{2240}(233, \cdot)\) None 0 8
2240.1.er \(\chi_{2240}(87, \cdot)\) None 0 8
2240.1.ew \(\chi_{2240}(151, \cdot)\) None 0 8
2240.1.ex \(\chi_{2240}(89, \cdot)\) None 0 8
2240.1.fa \(\chi_{2240}(37, \cdot)\) None 0 16
2240.1.fb \(\chi_{2240}(227, \cdot)\) None 0 16
2240.1.fc \(\chi_{2240}(179, \cdot)\) None 0 16
2240.1.fd \(\chi_{2240}(61, \cdot)\) None 0 16
2240.1.fe \(\chi_{2240}(11, \cdot)\) None 0 16
2240.1.ff \(\chi_{2240}(229, \cdot)\) None 0 16
2240.1.fm \(\chi_{2240}(3, \cdot)\) None 0 16
2240.1.fn \(\chi_{2240}(53, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2240))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2240)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1120))\)\(^{\oplus 2}\)