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Properties

Label 442.2
Level 442
Weight 2
Dimension 1981
Nonzero newspaces 20
Newform subspaces 71
Sturm bound 24192
Trace bound 15

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Defining parameters

Level: \( N \) = \( 442 = 2 \cdot 13 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 71 \)
Sturm bound: \(24192\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(442))\).

Total New Old
Modular forms 6432 1981 4451
Cusp forms 5665 1981 3684
Eisenstein series 767 0 767

Trace form

\( 1981 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 12 q^{6} + 16 q^{7} - 3 q^{8} + 7 q^{9} + O(q^{10}) \) \( 1981 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 12 q^{6} + 16 q^{7} - 3 q^{8} + 7 q^{9} - 20 q^{10} - 20 q^{11} - 12 q^{12} - 37 q^{13} - 32 q^{14} - 72 q^{15} - 13 q^{16} - 12 q^{17} - 55 q^{18} - 28 q^{19} + 4 q^{20} - 56 q^{21} + 4 q^{22} + 16 q^{23} - 4 q^{24} - 9 q^{25} + 23 q^{26} + 16 q^{28} - 28 q^{29} + 24 q^{30} - 48 q^{31} + 3 q^{32} - 40 q^{33} + 11 q^{34} - 64 q^{35} - 9 q^{36} - 12 q^{37} - 28 q^{38} - 60 q^{39} + 18 q^{40} - 112 q^{41} - 72 q^{42} - 68 q^{43} - 76 q^{44} - 84 q^{45} - 40 q^{46} - 112 q^{47} + 12 q^{48} - 21 q^{49} - 73 q^{50} - 60 q^{51} - 19 q^{52} - 46 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{57} - 28 q^{58} - 76 q^{59} - 40 q^{60} + 12 q^{61} - 72 q^{62} - 128 q^{63} - 3 q^{64} - 48 q^{65} + 32 q^{66} + 20 q^{67} + 24 q^{68} - 80 q^{69} + 8 q^{70} - 24 q^{71} - 49 q^{72} - 122 q^{73} - 36 q^{74} - 148 q^{75} + 4 q^{76} - 112 q^{77} - 76 q^{78} - 112 q^{79} - 20 q^{80} - 93 q^{81} - 112 q^{82} - 84 q^{83} - 24 q^{84} - 177 q^{85} + 20 q^{86} - 168 q^{87} - 28 q^{88} - 114 q^{89} - 22 q^{90} - 96 q^{91} - 8 q^{92} - 96 q^{93} - 104 q^{94} - 72 q^{95} + 12 q^{96} - 98 q^{97} + 3 q^{98} - 116 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(442))\)

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
442.2.a \(\chi_{442}(1, \cdot)\) 442.2.a.a 1 1
442.2.a.b 1
442.2.a.c 1
442.2.a.d 1
442.2.a.e 1
442.2.a.f 2
442.2.a.g 2
442.2.a.h 3
442.2.a.i 3
442.2.b \(\chi_{442}(339, \cdot)\) 442.2.b.a 2 1
442.2.b.b 2
442.2.b.c 4
442.2.b.d 4
442.2.b.e 6
442.2.c \(\chi_{442}(441, \cdot)\) 442.2.c.a 4 1
442.2.c.b 16
442.2.d \(\chi_{442}(103, \cdot)\) 442.2.d.a 4 1
442.2.d.b 6
442.2.d.c 6
442.2.e \(\chi_{442}(35, \cdot)\) 442.2.e.a 2 2
442.2.e.b 2
442.2.e.c 8
442.2.e.d 8
442.2.e.e 8
442.2.e.f 12
442.2.h \(\chi_{442}(157, \cdot)\) 442.2.h.a 2 2
442.2.h.b 2
442.2.h.c 2
442.2.h.d 2
442.2.h.e 2
442.2.h.f 2
442.2.h.g 2
442.2.h.h 2
442.2.h.i 2
442.2.h.j 4
442.2.h.k 4
442.2.h.l 10
442.2.i \(\chi_{442}(259, \cdot)\) 442.2.i.a 2 2
442.2.i.b 2
442.2.i.c 18
442.2.i.d 18
442.2.l \(\chi_{442}(69, \cdot)\) 442.2.l.a 16 2
442.2.l.b 24
442.2.m \(\chi_{442}(237, \cdot)\) 442.2.m.a 20 2
442.2.m.b 24
442.2.n \(\chi_{442}(101, \cdot)\) 442.2.n.a 40 2
442.2.p \(\chi_{442}(53, \cdot)\) 442.2.p.a 4 4
442.2.p.b 8
442.2.p.c 12
442.2.p.d 12
442.2.p.e 16
442.2.p.f 20
442.2.q \(\chi_{442}(25, \cdot)\) 442.2.q.a 44 4
442.2.q.b 44
442.2.u \(\chi_{442}(225, \cdot)\) 442.2.u.a 40 4
442.2.u.b 40
442.2.v \(\chi_{442}(55, \cdot)\) 442.2.v.a 8 4
442.2.v.b 32
442.2.v.c 48
442.2.y \(\chi_{442}(57, \cdot)\) 442.2.y.a 80 8
442.2.y.b 88
442.2.bb \(\chi_{442}(5, \cdot)\) 442.2.bb.a 80 8
442.2.bb.b 88
442.2.bd \(\chi_{442}(9, \cdot)\) 442.2.bd.a 80 8
442.2.bd.b 80
442.2.be \(\chi_{442}(43, \cdot)\) 442.2.be.a 88 8
442.2.be.b 88
442.2.bg \(\chi_{442}(37, \cdot)\) 442.2.bg.a 160 16
442.2.bg.b 176
442.2.bj \(\chi_{442}(7, \cdot)\) 442.2.bj.a 160 16
442.2.bj.b 176

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(442))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(442)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(221))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(442))\)\(^{\oplus 1}\)