Properties

Label 670.2
Level 670
Weight 2
Dimension 4115
Nonzero newspaces 12
Newforms 39
Sturm bound 53856
Trace bound 4

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Defining parameters

Level: \( N \) = \( 670 = 2 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newforms: \( 39 \)
Sturm bound: \(53856\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(670))\).

Total New Old
Modular forms 13992 4115 9877
Cusp forms 12937 4115 8822
Eisenstein series 1055 0 1055

Trace form

\( 4115q + q^{2} + 4q^{3} + q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} + O(q^{10}) \) \( 4115q + q^{2} + 4q^{3} + q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} + q^{10} + 12q^{11} + 4q^{12} + 14q^{13} + 8q^{14} + 4q^{15} + q^{16} + 18q^{17} + 13q^{18} + 20q^{19} + q^{20} + 32q^{21} + 12q^{22} + 24q^{23} + 4q^{24} + q^{25} + 14q^{26} + 40q^{27} + 8q^{28} + 30q^{29} + 4q^{30} + 32q^{31} + q^{32} + 48q^{33} + 18q^{34} + 8q^{35} + 13q^{36} + 38q^{37} + 20q^{38} + 56q^{39} + q^{40} + 42q^{41} + 32q^{42} + 44q^{43} + 12q^{44} + 13q^{45} + 24q^{46} + 48q^{47} + 4q^{48} + 57q^{49} + q^{50} + 72q^{51} - 30q^{52} - 78q^{53} - 158q^{54} - 186q^{55} + 8q^{56} - 228q^{57} - 234q^{58} - 204q^{59} - 128q^{60} - 466q^{61} - 100q^{62} - 468q^{63} + q^{64} - 250q^{65} - 480q^{66} - 197q^{67} - 114q^{68} - 168q^{69} - 256q^{70} - 456q^{71} + 13q^{72} - 498q^{73} - 94q^{74} - 260q^{75} - 244q^{76} - 168q^{77} - 208q^{78} - 228q^{79} + q^{80} - 275q^{81} - 156q^{82} - 48q^{83} - 12q^{84} + 18q^{85} + 44q^{86} + 120q^{87} + 12q^{88} + 90q^{89} + 13q^{90} + 112q^{91} + 24q^{92} + 128q^{93} + 48q^{94} + 20q^{95} + 4q^{96} + 98q^{97} + 57q^{98} + 156q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(670))\)

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
670.2.a \(\chi_{670}(1, \cdot)\) 670.2.a.a 1 1
670.2.a.b 1
670.2.a.c 1
670.2.a.d 1
670.2.a.e 2
670.2.a.f 2
670.2.a.g 3
670.2.a.h 3
670.2.a.i 3
670.2.a.j 4
670.2.c \(\chi_{670}(269, \cdot)\) 670.2.c.a 10 1
670.2.c.b 24
670.2.e \(\chi_{670}(171, \cdot)\) 670.2.e.a 2 2
670.2.e.b 2
670.2.e.c 2
670.2.e.d 2
670.2.e.e 4
670.2.e.f 4
670.2.e.g 6
670.2.e.h 6
670.2.e.i 8
670.2.e.j 12
670.2.f \(\chi_{670}(133, \cdot)\) 670.2.f.a 68 2
670.2.h \(\chi_{670}(29, \cdot)\) 670.2.h.a 4 2
670.2.h.b 12
670.2.h.c 52
670.2.k \(\chi_{670}(81, \cdot)\) 670.2.k.a 40 10
670.2.k.b 50
670.2.k.c 50
670.2.k.d 60
670.2.m \(\chi_{670}(97, \cdot)\) 670.2.m.a 136 4
670.2.o \(\chi_{670}(9, \cdot)\) 670.2.o.a 340 10
670.2.q \(\chi_{670}(21, \cdot)\) 670.2.q.a 100 20
670.2.q.b 120
670.2.q.c 120
670.2.q.d 140
670.2.s \(\chi_{670}(3, \cdot)\) 670.2.s.a 680 20
670.2.v \(\chi_{670}(19, \cdot)\) 670.2.v.a 680 20
670.2.w \(\chi_{670}(7, \cdot)\) 670.2.w.a 1360 40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(670))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(670)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(335))\)\(^{\oplus 2}\)