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Properties

Label 434.2
Level 434
Weight 2
Dimension 1839
Nonzero newspaces 20
Newform subspaces 84
Sturm bound 23040
Trace bound 6

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Defining parameters

Level: \( N \) = \( 434 = 2 \cdot 7 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 84 \)
Sturm bound: \(23040\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(434))\).

Total New Old
Modular forms 6120 1839 4281
Cusp forms 5401 1839 3562
Eisenstein series 719 0 719

Trace form

\( 1839 q + 3 q^{2} + 8 q^{3} - q^{4} + 6 q^{5} - q^{7} + 3 q^{8} + 11 q^{9} + O(q^{10}) \) \( 1839 q + 3 q^{2} + 8 q^{3} - q^{4} + 6 q^{5} - q^{7} + 3 q^{8} + 11 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{12} + 22 q^{13} + 3 q^{14} + 24 q^{15} - q^{16} + 6 q^{17} + 15 q^{18} + 16 q^{19} + 6 q^{20} - 2 q^{21} - 48 q^{22} - 36 q^{23} - 99 q^{25} - 54 q^{26} - 148 q^{27} - 41 q^{28} - 78 q^{29} - 96 q^{30} - 85 q^{31} + 3 q^{32} - 72 q^{33} - 90 q^{34} - 54 q^{35} - 69 q^{36} - 146 q^{37} - 36 q^{38} - 100 q^{39} + 6 q^{40} - 30 q^{41} - 30 q^{42} + 8 q^{43} + 12 q^{44} + 78 q^{45} + 24 q^{46} + 72 q^{47} + 8 q^{48} - 31 q^{49} + 21 q^{50} - 84 q^{51} + 22 q^{52} - 18 q^{53} + 48 q^{54} - 48 q^{55} + 3 q^{56} - 92 q^{57} + 18 q^{58} + 12 q^{59} + 24 q^{60} - 134 q^{61} + 27 q^{62} - 109 q^{63} - q^{64} - 96 q^{65} + 48 q^{66} + 16 q^{67} + 6 q^{68} - 84 q^{69} + 6 q^{70} - 48 q^{71} + 15 q^{72} + 10 q^{73} + 42 q^{74} - 136 q^{75} - 4 q^{76} - 108 q^{77} - 108 q^{78} - 76 q^{79} - 54 q^{80} - 97 q^{81} - 66 q^{82} - 324 q^{83} - 52 q^{84} - 132 q^{85} - 180 q^{86} - 144 q^{87} - 108 q^{88} - 198 q^{89} - 282 q^{90} - 108 q^{91} + 24 q^{92} - 364 q^{93} - 96 q^{94} - 360 q^{95} - 142 q^{97} - 177 q^{98} - 144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(434))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
434.2.a \(\chi_{434}(1, \cdot)\) 434.2.a.a 1 1
434.2.a.b 1
434.2.a.c 1
434.2.a.d 1
434.2.a.e 1
434.2.a.f 2
434.2.a.g 2
434.2.a.h 3
434.2.a.i 3
434.2.d \(\chi_{434}(433, \cdot)\) 434.2.d.a 2 1
434.2.d.b 2
434.2.d.c 2
434.2.d.d 2
434.2.d.e 8
434.2.d.f 8
434.2.e \(\chi_{434}(211, \cdot)\) 434.2.e.a 4 2
434.2.e.b 4
434.2.e.c 8
434.2.e.d 8
434.2.e.e 8
434.2.f \(\chi_{434}(249, \cdot)\) 434.2.f.a 2 2
434.2.f.b 2
434.2.f.c 4
434.2.f.d 6
434.2.f.e 6
434.2.f.f 6
434.2.f.g 14
434.2.g \(\chi_{434}(67, \cdot)\) 434.2.g.a 2 2
434.2.g.b 2
434.2.g.c 8
434.2.g.d 14
434.2.g.e 18
434.2.h \(\chi_{434}(25, \cdot)\) 434.2.h.a 2 2
434.2.h.b 2
434.2.h.c 8
434.2.h.d 14
434.2.h.e 18
434.2.i \(\chi_{434}(225, \cdot)\) 434.2.i.a 4 4
434.2.i.b 12
434.2.i.c 16
434.2.i.d 16
434.2.i.e 16
434.2.l \(\chi_{434}(285, \cdot)\) 434.2.l.a 2 2
434.2.l.b 2
434.2.l.c 10
434.2.l.d 10
434.2.l.e 20
434.2.m \(\chi_{434}(181, \cdot)\) 434.2.m.a 2 2
434.2.m.b 2
434.2.m.c 2
434.2.m.d 2
434.2.m.e 16
434.2.m.f 16
434.2.n \(\chi_{434}(61, \cdot)\) 434.2.n.a 4 2
434.2.n.b 16
434.2.n.c 20
434.2.u \(\chi_{434}(243, \cdot)\) 434.2.u.a 2 2
434.2.u.b 2
434.2.u.c 10
434.2.u.d 10
434.2.u.e 20
434.2.v \(\chi_{434}(27, \cdot)\) 434.2.v.a 48 4
434.2.v.b 48
434.2.y \(\chi_{434}(9, \cdot)\) 434.2.y.a 88 8
434.2.y.b 88
434.2.z \(\chi_{434}(107, \cdot)\) 434.2.z.a 88 8
434.2.z.b 88
434.2.ba \(\chi_{434}(39, \cdot)\) 434.2.ba.a 8 8
434.2.ba.b 72
434.2.ba.c 80
434.2.bb \(\chi_{434}(71, \cdot)\) 434.2.bb.a 8 8
434.2.bb.b 24
434.2.bb.c 32
434.2.bb.d 32
434.2.bb.e 32
434.2.bc \(\chi_{434}(3, \cdot)\) 434.2.bc.a 88 8
434.2.bc.b 88
434.2.bj \(\chi_{434}(89, \cdot)\) 434.2.bj.a 80 8
434.2.bj.b 80
434.2.bk \(\chi_{434}(13, \cdot)\) 434.2.bk.a 16 8
434.2.bk.b 64
434.2.bk.c 80
434.2.bl \(\chi_{434}(73, \cdot)\) 434.2.bl.a 88 8
434.2.bl.b 88

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(434))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(434)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(217))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(434))\)\(^{\oplus 1}\)