Properties

Label 370.2
Level 370
Weight 2
Dimension 1255
Nonzero newspaces 18
Newform subspaces 70
Sturm bound 16416
Trace bound 7

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Defining parameters

Level: \( N \) = \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Newform subspaces: \( 70 \)
Sturm bound: \(16416\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(370))\).

Total New Old
Modular forms 4392 1255 3137
Cusp forms 3817 1255 2562
Eisenstein series 575 0 575

Trace form

\( 1255q + q^{2} + 4q^{3} + q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} + O(q^{10}) \) \( 1255q + q^{2} + 4q^{3} + q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} + q^{10} + 12q^{11} + 4q^{12} + 14q^{13} + 8q^{14} + 4q^{15} + q^{16} + 18q^{17} + 13q^{18} + 20q^{19} + q^{20} + 32q^{21} + 12q^{22} + 24q^{23} + 4q^{24} + q^{25} - 4q^{26} - 56q^{27} - 16q^{28} - 42q^{29} - 68q^{30} - 184q^{31} + q^{32} - 96q^{33} - 126q^{34} - 100q^{35} - 77q^{36} - 131q^{37} - 52q^{38} - 112q^{39} - 44q^{40} - 174q^{41} - 112q^{42} - 100q^{43} + 12q^{44} - 95q^{45} - 120q^{46} - 24q^{47} - 20q^{48} - 39q^{49} - 8q^{50} + 72q^{51} + 14q^{52} + 54q^{53} + 40q^{54} + 12q^{55} + 8q^{56} + 80q^{57} + 30q^{58} - 12q^{59} + 4q^{60} - 28q^{61} + 32q^{62} - 112q^{63} + q^{64} - 67q^{65} + 48q^{66} - 4q^{67} + 18q^{68} - 192q^{69} + 8q^{70} - 72q^{71} + 13q^{72} - 70q^{73} + 37q^{74} - 176q^{75} + 20q^{76} - 48q^{77} + 56q^{78} - 64q^{79} + q^{80} - 167q^{81} + 42q^{82} + 12q^{83} + 32q^{84} - 63q^{85} + 44q^{86} - 96q^{87} + 12q^{88} + 13q^{90} + 16q^{91} - 48q^{92} - 88q^{93} - 96q^{94} - 124q^{95} + 4q^{96} - 190q^{97} - 231q^{98} - 204q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(370))\)

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
370.2.a \(\chi_{370}(1, \cdot)\) 370.2.a.a 1 1
370.2.a.b 1
370.2.a.c 1
370.2.a.d 1
370.2.a.e 2
370.2.a.f 2
370.2.a.g 3
370.2.b \(\chi_{370}(149, \cdot)\) 370.2.b.a 2 1
370.2.b.b 2
370.2.b.c 4
370.2.b.d 10
370.2.c \(\chi_{370}(369, \cdot)\) 370.2.c.a 10 1
370.2.c.b 10
370.2.d \(\chi_{370}(221, \cdot)\) 370.2.d.a 2 1
370.2.d.b 2
370.2.d.c 6
370.2.e \(\chi_{370}(121, \cdot)\) 370.2.e.a 2 2
370.2.e.b 2
370.2.e.c 2
370.2.e.d 4
370.2.e.e 4
370.2.e.f 6
370.2.g \(\chi_{370}(43, \cdot)\) 370.2.g.a 2 2
370.2.g.b 2
370.2.g.c 4
370.2.g.d 10
370.2.g.e 20
370.2.h \(\chi_{370}(117, \cdot)\) 370.2.h.a 2 2
370.2.h.b 2
370.2.h.c 4
370.2.h.d 10
370.2.h.e 20
370.2.l \(\chi_{370}(11, \cdot)\) 370.2.l.a 4 2
370.2.l.b 4
370.2.l.c 12
370.2.m \(\chi_{370}(159, \cdot)\) 370.2.m.a 4 2
370.2.m.b 4
370.2.m.c 16
370.2.m.d 16
370.2.n \(\chi_{370}(269, \cdot)\) 370.2.n.a 4 2
370.2.n.b 4
370.2.n.c 4
370.2.n.d 4
370.2.n.e 8
370.2.n.f 12
370.2.o \(\chi_{370}(71, \cdot)\) 370.2.o.a 18 6
370.2.o.b 18
370.2.o.c 24
370.2.o.d 24
370.2.q \(\chi_{370}(97, \cdot)\) 370.2.q.a 4 4
370.2.q.b 4
370.2.q.c 8
370.2.q.d 12
370.2.q.e 16
370.2.q.f 32
370.2.r \(\chi_{370}(23, \cdot)\) 370.2.r.a 4 4
370.2.r.b 4
370.2.r.c 8
370.2.r.d 12
370.2.r.e 16
370.2.r.f 32
370.2.v \(\chi_{370}(99, \cdot)\) 370.2.v.a 60 6
370.2.v.b 60
370.2.w \(\chi_{370}(21, \cdot)\) 370.2.w.a 36 6
370.2.w.b 48
370.2.x \(\chi_{370}(9, \cdot)\) 370.2.x.a 108 6
370.2.ba \(\chi_{370}(17, \cdot)\) 370.2.ba.a 108 12
370.2.ba.b 120
370.2.bd \(\chi_{370}(13, \cdot)\) 370.2.bd.a 108 12
370.2.bd.b 120

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(370))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(370)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 2}\)