Properties

Label 760.2
Level 760
Weight 2
Dimension 8656
Nonzero newspaces 27
Newform subspaces 68
Sturm bound 69120
Trace bound 9

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Defining parameters

Level: \( N \) = \( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 27 \)
Newform subspaces: \( 68 \)
Sturm bound: \(69120\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(760))\).

Total New Old
Modular forms 18144 9064 9080
Cusp forms 16417 8656 7761
Eisenstein series 1727 408 1319

Trace form

\( 8656q - 28q^{2} - 28q^{3} - 28q^{4} + 2q^{5} - 92q^{6} - 20q^{7} - 28q^{8} - 46q^{9} + O(q^{10}) \) \( 8656q - 28q^{2} - 28q^{3} - 28q^{4} + 2q^{5} - 92q^{6} - 20q^{7} - 28q^{8} - 46q^{9} - 46q^{10} - 84q^{11} - 52q^{12} + 4q^{13} - 52q^{14} - 62q^{15} - 124q^{16} - 60q^{17} - 84q^{18} - 48q^{19} - 140q^{20} - 16q^{21} - 68q^{22} - 36q^{23} - 84q^{24} - 82q^{25} - 124q^{26} - 34q^{27} - 20q^{28} + 48q^{29} - 54q^{30} - 72q^{31} + 12q^{32} + 52q^{33} + 36q^{34} - 34q^{35} - 28q^{36} + 24q^{37} - 12q^{38} + 20q^{39} + 34q^{40} - 144q^{41} + 12q^{42} - 4q^{43} - 4q^{44} + 56q^{45} - 44q^{46} - 48q^{47} - 20q^{48} - 50q^{49} - 86q^{50} - 106q^{51} - 76q^{52} - 12q^{53} - 192q^{54} - 110q^{55} - 204q^{56} - 88q^{57} - 160q^{58} - 76q^{59} - 170q^{60} + 8q^{61} - 328q^{62} - 164q^{63} - 388q^{64} - 190q^{65} - 428q^{66} - 212q^{67} - 328q^{68} - 16q^{69} - 270q^{70} - 168q^{71} - 552q^{72} - 286q^{73} - 284q^{74} + 44q^{75} - 468q^{76} - 76q^{77} - 268q^{78} - 128q^{79} - 150q^{80} - 384q^{81} - 504q^{82} - 24q^{83} - 404q^{84} - 4q^{85} - 376q^{86} - 156q^{87} - 324q^{88} - 208q^{89} - 190q^{90} - 220q^{91} - 184q^{92} - 36q^{93} - 172q^{94} - 6q^{95} - 312q^{96} + 28q^{97} - 60q^{98} + 98q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(760))\)

We only show spaces with even 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
760.2.a \(\chi_{760}(1, \cdot)\) 760.2.a.a 1 1
760.2.a.b 1
760.2.a.c 1
760.2.a.d 1
760.2.a.e 1
760.2.a.f 2
760.2.a.g 2
760.2.a.h 3
760.2.a.i 3
760.2.a.j 3
760.2.d \(\chi_{760}(609, \cdot)\) 760.2.d.a 2 1
760.2.d.b 4
760.2.d.c 4
760.2.d.d 4
760.2.d.e 12
760.2.e \(\chi_{760}(531, \cdot)\) 760.2.e.a 80 1
760.2.f \(\chi_{760}(381, \cdot)\) 760.2.f.a 28 1
760.2.f.b 44
760.2.g \(\chi_{760}(759, \cdot)\) None 0 1
760.2.j \(\chi_{760}(151, \cdot)\) None 0 1
760.2.k \(\chi_{760}(229, \cdot)\) 760.2.k.a 108 1
760.2.p \(\chi_{760}(379, \cdot)\) 760.2.p.a 4 1
760.2.p.b 4
760.2.p.c 4
760.2.p.d 8
760.2.p.e 8
760.2.p.f 8
760.2.p.g 8
760.2.p.h 16
760.2.p.i 56
760.2.q \(\chi_{760}(121, \cdot)\) 760.2.q.a 2 2
760.2.q.b 2
760.2.q.c 2
760.2.q.d 8
760.2.q.e 8
760.2.q.f 8
760.2.q.g 10
760.2.t \(\chi_{760}(37, \cdot)\) 760.2.t.a 232 2
760.2.u \(\chi_{760}(343, \cdot)\) None 0 2
760.2.v \(\chi_{760}(113, \cdot)\) 760.2.v.a 12 2
760.2.v.b 48
760.2.w \(\chi_{760}(267, \cdot)\) 760.2.w.a 2 2
760.2.w.b 2
760.2.w.c 104
760.2.w.d 108
760.2.z \(\chi_{760}(349, \cdot)\) 760.2.z.a 232 2
760.2.ba \(\chi_{760}(31, \cdot)\) None 0 2
760.2.bf \(\chi_{760}(179, \cdot)\) 760.2.bf.a 8 2
760.2.bf.b 224
760.2.bi \(\chi_{760}(331, \cdot)\) 760.2.bi.a 160 2
760.2.bj \(\chi_{760}(49, \cdot)\) 760.2.bj.a 4 2
760.2.bj.b 56
760.2.bk \(\chi_{760}(559, \cdot)\) None 0 2
760.2.bl \(\chi_{760}(501, \cdot)\) 760.2.bl.a 4 2
760.2.bl.b 4
760.2.bl.c 152
760.2.bo \(\chi_{760}(81, \cdot)\) 760.2.bo.a 24 6
760.2.bo.b 30
760.2.bo.c 30
760.2.bo.d 36
760.2.bp \(\chi_{760}(293, \cdot)\) 760.2.bp.a 464 4
760.2.bq \(\chi_{760}(7, \cdot)\) None 0 4
760.2.bv \(\chi_{760}(217, \cdot)\) 760.2.bv.a 120 4
760.2.bw \(\chi_{760}(83, \cdot)\) 760.2.bw.a 8 4
760.2.bw.b 456
760.2.bx \(\chi_{760}(59, \cdot)\) 760.2.bx.a 24 6
760.2.bx.b 672
760.2.cc \(\chi_{760}(61, \cdot)\) 760.2.cc.a 480 6
760.2.cd \(\chi_{760}(79, \cdot)\) None 0 6
760.2.cg \(\chi_{760}(9, \cdot)\) 760.2.cg.a 180 6
760.2.ch \(\chi_{760}(51, \cdot)\) 760.2.ch.a 480 6
760.2.ci \(\chi_{760}(71, \cdot)\) None 0 6
760.2.cj \(\chi_{760}(149, \cdot)\) 760.2.cj.a 696 6
760.2.co \(\chi_{760}(33, \cdot)\) 760.2.co.a 360 12
760.2.cp \(\chi_{760}(43, \cdot)\) 760.2.cp.a 1392 12
760.2.cs \(\chi_{760}(13, \cdot)\) 760.2.cs.a 1392 12
760.2.ct \(\chi_{760}(23, \cdot)\) None 0 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(760))\) into lower level spaces

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