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Properties

Label 760.1
Level 760
Weight 1
Dimension 28
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 34560
Trace bound 3

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Defining parameters

Level: \( N \) = \( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(34560\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(760))\).

Total New Old
Modular forms 944 232 712
Cusp forms 80 28 52
Eisenstein series 864 204 660

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 4 0

Trace form

\( 28 q + 2 q^{3} - 2 q^{4} - 10 q^{9} + O(q^{10}) \) \( 28 q + 2 q^{3} - 2 q^{4} - 10 q^{9} - 2 q^{10} + 14 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{19} - 2 q^{23} + 8 q^{24} - 8 q^{25} + 22 q^{26} - 8 q^{30} - 4 q^{31} + 2 q^{33} - 4 q^{35} - 10 q^{36} - 4 q^{37} - 2 q^{40} - 4 q^{41} - 2 q^{43} - 12 q^{44} - 4 q^{45} - 4 q^{46} + 2 q^{49} + 2 q^{53} - 8 q^{54} - 4 q^{56} - 4 q^{57} - 4 q^{59} + 2 q^{61} - 2 q^{64} + 14 q^{65} + 8 q^{66} - 2 q^{71} + 2 q^{73} - 4 q^{74} + 4 q^{75} - 2 q^{76} + 8 q^{80} + 4 q^{81} - 4 q^{83} + 4 q^{87} + 14 q^{89} - 2 q^{90} - 8 q^{91} - 2 q^{93} - 4 q^{94} + 12 q^{95} + 8 q^{96} + 2 q^{97} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(760))\)

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
760.1.b \(\chi_{760}(189, \cdot)\) 760.1.b.a 8 1
760.1.c \(\chi_{760}(191, \cdot)\) None 0 1
760.1.h \(\chi_{760}(721, \cdot)\) None 0 1
760.1.i \(\chi_{760}(419, \cdot)\) None 0 1
760.1.l \(\chi_{760}(571, \cdot)\) None 0 1
760.1.m \(\chi_{760}(569, \cdot)\) None 0 1
760.1.n \(\chi_{760}(39, \cdot)\) None 0 1
760.1.o \(\chi_{760}(341, \cdot)\) None 0 1
760.1.r \(\chi_{760}(77, \cdot)\) None 0 2
760.1.s \(\chi_{760}(303, \cdot)\) None 0 2
760.1.x \(\chi_{760}(153, \cdot)\) None 0 2
760.1.y \(\chi_{760}(227, \cdot)\) None 0 2
760.1.bb \(\chi_{760}(369, \cdot)\) None 0 2
760.1.bc \(\chi_{760}(11, \cdot)\) None 0 2
760.1.bd \(\chi_{760}(141, \cdot)\) None 0 2
760.1.be \(\chi_{760}(159, \cdot)\) None 0 2
760.1.bg \(\chi_{760}(311, \cdot)\) None 0 2
760.1.bh \(\chi_{760}(69, \cdot)\) None 0 2
760.1.bm \(\chi_{760}(539, \cdot)\) 760.1.bm.a 2 2
760.1.bm.b 2
760.1.bn \(\chi_{760}(521, \cdot)\) None 0 2
760.1.br \(\chi_{760}(197, \cdot)\) None 0 4
760.1.bs \(\chi_{760}(103, \cdot)\) None 0 4
760.1.bt \(\chi_{760}(273, \cdot)\) 760.1.bt.a 4 4
760.1.bu \(\chi_{760}(27, \cdot)\) None 0 4
760.1.by \(\chi_{760}(41, \cdot)\) None 0 6
760.1.bz \(\chi_{760}(99, \cdot)\) 760.1.bz.a 6 6
760.1.bz.b 6
760.1.ca \(\chi_{760}(119, \cdot)\) None 0 6
760.1.cb \(\chi_{760}(21, \cdot)\) None 0 6
760.1.ce \(\chi_{760}(131, \cdot)\) None 0 6
760.1.cf \(\chi_{760}(89, \cdot)\) None 0 6
760.1.ck \(\chi_{760}(29, \cdot)\) None 0 6
760.1.cl \(\chi_{760}(111, \cdot)\) None 0 6
760.1.cm \(\chi_{760}(17, \cdot)\) None 0 12
760.1.cn \(\chi_{760}(3, \cdot)\) None 0 12
760.1.cq \(\chi_{760}(93, \cdot)\) None 0 12
760.1.cr \(\chi_{760}(127, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(760))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(760)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(760))\)\(^{\oplus 1}\)