Properties

Label 1960.1
Level 1960
Weight 1
Dimension 88
Nonzero newspaces 9
Newform subspaces 15
Sturm bound 225792
Trace bound 11

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Defining parameters

Level: \( N \) = \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 15 \)
Sturm bound: \(225792\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1960))\).

Total New Old
Modular forms 3238 670 2568
Cusp forms 358 88 270
Eisenstein series 2880 582 2298

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 76 0 12 0

Trace form

\( 88q + 6q^{4} + 6q^{9} + O(q^{10}) \) \( 88q + 6q^{4} + 6q^{9} + 2q^{10} - 8q^{11} - 8q^{15} - 2q^{16} - 8q^{19} + 2q^{25} - 8q^{26} + 4q^{30} - 14q^{36} - 8q^{39} + 2q^{40} + 4q^{41} - 12q^{43} + 34q^{44} - 8q^{46} - 6q^{49} - 8q^{50} + 36q^{56} - 36q^{57} + 4q^{59} - 4q^{60} - 6q^{64} - 12q^{65} - 8q^{74} + 4q^{76} - 24q^{78} + 6q^{81} - 12q^{85} + 4q^{89} - 10q^{90} + 24q^{92} - 8q^{94} + 4q^{95} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1960))\)

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
1960.1.c \(\chi_{1960}(1469, \cdot)\) None 0 1
1960.1.d \(\chi_{1960}(1471, \cdot)\) None 0 1
1960.1.f \(\chi_{1960}(881, \cdot)\) None 0 1
1960.1.i \(\chi_{1960}(99, \cdot)\) 1960.1.i.a 1 1
1960.1.i.b 1
1960.1.i.c 1
1960.1.i.d 1
1960.1.j \(\chi_{1960}(1079, \cdot)\) None 0 1
1960.1.m \(\chi_{1960}(1861, \cdot)\) None 0 1
1960.1.o \(\chi_{1960}(491, \cdot)\) None 0 1
1960.1.p \(\chi_{1960}(489, \cdot)\) None 0 1
1960.1.r \(\chi_{1960}(783, \cdot)\) None 0 2
1960.1.u \(\chi_{1960}(197, \cdot)\) 1960.1.u.a 8 2
1960.1.v \(\chi_{1960}(393, \cdot)\) 1960.1.v.a 4 2
1960.1.y \(\chi_{1960}(587, \cdot)\) None 0 2
1960.1.z \(\chi_{1960}(851, \cdot)\) None 0 2
1960.1.bb \(\chi_{1960}(129, \cdot)\) None 0 2
1960.1.bd \(\chi_{1960}(79, \cdot)\) None 0 2
1960.1.be \(\chi_{1960}(901, \cdot)\) None 0 2
1960.1.bh \(\chi_{1960}(521, \cdot)\) None 0 2
1960.1.bi \(\chi_{1960}(459, \cdot)\) 1960.1.bi.a 2 2
1960.1.bi.b 2
1960.1.bk \(\chi_{1960}(509, \cdot)\) 1960.1.bk.a 8 2
1960.1.bn \(\chi_{1960}(471, \cdot)\) None 0 2
1960.1.bq \(\chi_{1960}(227, \cdot)\) None 0 4
1960.1.br \(\chi_{1960}(177, \cdot)\) 1960.1.br.a 8 4
1960.1.bu \(\chi_{1960}(373, \cdot)\) 1960.1.bu.a 16 4
1960.1.bv \(\chi_{1960}(423, \cdot)\) None 0 4
1960.1.bx \(\chi_{1960}(209, \cdot)\) None 0 6
1960.1.bz \(\chi_{1960}(211, \cdot)\) None 0 6
1960.1.cb \(\chi_{1960}(181, \cdot)\) None 0 6
1960.1.cc \(\chi_{1960}(239, \cdot)\) None 0 6
1960.1.cf \(\chi_{1960}(379, \cdot)\) 1960.1.cf.a 6 6
1960.1.cf.b 6
1960.1.cg \(\chi_{1960}(41, \cdot)\) None 0 6
1960.1.ci \(\chi_{1960}(71, \cdot)\) None 0 6
1960.1.cl \(\chi_{1960}(69, \cdot)\) None 0 6
1960.1.co \(\chi_{1960}(57, \cdot)\) None 0 12
1960.1.cp \(\chi_{1960}(27, \cdot)\) None 0 12
1960.1.cs \(\chi_{1960}(167, \cdot)\) None 0 12
1960.1.ct \(\chi_{1960}(253, \cdot)\) None 0 12
1960.1.cw \(\chi_{1960}(151, \cdot)\) None 0 12
1960.1.cx \(\chi_{1960}(229, \cdot)\) None 0 12
1960.1.cz \(\chi_{1960}(179, \cdot)\) 1960.1.cz.a 12 12
1960.1.cz.b 12
1960.1.dc \(\chi_{1960}(201, \cdot)\) None 0 12
1960.1.dd \(\chi_{1960}(61, \cdot)\) None 0 12
1960.1.dg \(\chi_{1960}(39, \cdot)\) None 0 12
1960.1.dh \(\chi_{1960}(89, \cdot)\) None 0 12
1960.1.di \(\chi_{1960}(11, \cdot)\) None 0 12
1960.1.dk \(\chi_{1960}(37, \cdot)\) None 0 24
1960.1.dn \(\chi_{1960}(47, \cdot)\) None 0 24
1960.1.do \(\chi_{1960}(3, \cdot)\) None 0 24
1960.1.dr \(\chi_{1960}(137, \cdot)\) None 0 24

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1960))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1960)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(980))\)\(^{\oplus 2}\)