↑

Properties

Label 1980.1
Level 1980
Weight 1
Dimension 58
Nonzero newspaces 5
Newform subspaces 13
Sturm bound 207360
Trace bound 5

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 13 \)
Sturm bound: \(207360\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1980))\).

Total New Old
Modular forms 3420 546 2874
Cusp forms 220 58 162
Eisenstein series 3200 488 2712

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 42 0 16 0

Trace form

\( 58 q - 2 q^{3} - 8 q^{5} + 2 q^{9} + 6 q^{11} + 4 q^{15} + 8 q^{16} + 4 q^{22} - 24 q^{25} - 8 q^{27} + 4 q^{31} - 12 q^{33} - 16 q^{36} + 20 q^{37} + q^{45} - 12 q^{47} - 14 q^{49} + 5 q^{55} + 8 q^{56}+ \cdots - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1980))\)

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
1980.1.b \(\chi_{1980}(901, \cdot)\) None 0 1
1980.1.e \(\chi_{1980}(89, \cdot)\) None 0 1
1980.1.g \(\chi_{1980}(1979, \cdot)\) 1980.1.g.a 8 1
1980.1.g.b 8
1980.1.h \(\chi_{1980}(991, \cdot)\) None 0 1
1980.1.j \(\chi_{1980}(199, \cdot)\) None 0 1
1980.1.m \(\chi_{1980}(791, \cdot)\) None 0 1
1980.1.o \(\chi_{1980}(881, \cdot)\) None 0 1
1980.1.p \(\chi_{1980}(109, \cdot)\) 1980.1.p.a 2 1
1980.1.s \(\chi_{1980}(397, \cdot)\) None 0 2
1980.1.t \(\chi_{1980}(307, \cdot)\) None 0 2
1980.1.w \(\chi_{1980}(197, \cdot)\) None 0 2
1980.1.x \(\chi_{1980}(287, \cdot)\) None 0 2
1980.1.bb \(\chi_{1980}(221, \cdot)\) None 0 2
1980.1.bc \(\chi_{1980}(769, \cdot)\) 1980.1.bc.a 2 2
1980.1.bc.b 2
1980.1.bc.c 2
1980.1.bc.d 2
1980.1.bd \(\chi_{1980}(859, \cdot)\) None 0 2
1980.1.bg \(\chi_{1980}(131, \cdot)\) None 0 2
1980.1.bi \(\chi_{1980}(659, \cdot)\) None 0 2
1980.1.bj \(\chi_{1980}(331, \cdot)\) None 0 2
1980.1.bl \(\chi_{1980}(241, \cdot)\) None 0 2
1980.1.bo \(\chi_{1980}(749, \cdot)\) None 0 2
1980.1.bp \(\chi_{1980}(469, \cdot)\) None 0 4
1980.1.bq \(\chi_{1980}(521, \cdot)\) None 0 4
1980.1.bs \(\chi_{1980}(431, \cdot)\) None 0 4
1980.1.bv \(\chi_{1980}(379, \cdot)\) None 0 4
1980.1.bx \(\chi_{1980}(91, \cdot)\) None 0 4
1980.1.by \(\chi_{1980}(359, \cdot)\) None 0 4
1980.1.ca \(\chi_{1980}(269, \cdot)\) None 0 4
1980.1.cd \(\chi_{1980}(541, \cdot)\) None 0 4
1980.1.cf \(\chi_{1980}(43, \cdot)\) 1980.1.cf.a 8 4
1980.1.cf.b 8
1980.1.cg \(\chi_{1980}(133, \cdot)\) None 0 4
1980.1.cj \(\chi_{1980}(23, \cdot)\) None 0 4
1980.1.ck \(\chi_{1980}(857, \cdot)\) 1980.1.ck.a 4 4
1980.1.ck.b 4
1980.1.ck.c 4
1980.1.ck.d 4
1980.1.co \(\chi_{1980}(323, \cdot)\) None 0 8
1980.1.cp \(\chi_{1980}(17, \cdot)\) None 0 8
1980.1.cs \(\chi_{1980}(127, \cdot)\) None 0 8
1980.1.ct \(\chi_{1980}(37, \cdot)\) None 0 8
1980.1.cv \(\chi_{1980}(389, \cdot)\) None 0 8
1980.1.cy \(\chi_{1980}(61, \cdot)\) None 0 8
1980.1.da \(\chi_{1980}(31, \cdot)\) None 0 8
1980.1.db \(\chi_{1980}(239, \cdot)\) None 0 8
1980.1.dd \(\chi_{1980}(371, \cdot)\) None 0 8
1980.1.dg \(\chi_{1980}(499, \cdot)\) None 0 8
1980.1.dh \(\chi_{1980}(349, \cdot)\) None 0 8
1980.1.di \(\chi_{1980}(401, \cdot)\) None 0 8
1980.1.dl \(\chi_{1980}(173, \cdot)\) None 0 16
1980.1.dm \(\chi_{1980}(47, \cdot)\) None 0 16
1980.1.dp \(\chi_{1980}(97, \cdot)\) None 0 16
1980.1.dq \(\chi_{1980}(7, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1980))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1980)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(990))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1980))\)\(^{\oplus 1}\)