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Properties

Label 858.2
Level 858
Weight 2
Dimension 4893
Nonzero newspaces 24
Newform subspaces 103
Sturm bound 80640
Trace bound 9

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Defining parameters

Level: \( N \) = \( 858 = 2 \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 103 \)
Sturm bound: \(80640\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(858))\).

Total New Old
Modular forms 21120 4893 16227
Cusp forms 19201 4893 14308
Eisenstein series 1919 0 1919

Trace form

\( 4893 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 18 q^{5} + 7 q^{6} + 32 q^{7} + 9 q^{8} + 45 q^{9} + O(q^{10}) \) \( 4893 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 18 q^{5} + 7 q^{6} + 32 q^{7} + 9 q^{8} + 45 q^{9} + 82 q^{10} + 41 q^{11} + 25 q^{12} + 89 q^{13} + 64 q^{14} + 90 q^{15} + 13 q^{16} + 86 q^{17} + 19 q^{18} + 112 q^{19} - 6 q^{20} + 72 q^{21} - 23 q^{22} + 16 q^{23} - 13 q^{24} + 47 q^{25} - 27 q^{26} + 9 q^{27} - 24 q^{28} + 10 q^{29} - 126 q^{30} - 8 q^{31} - 3 q^{32} - 125 q^{33} - 54 q^{34} - 56 q^{35} - 61 q^{36} - 102 q^{37} - 60 q^{38} - 125 q^{39} - 18 q^{40} - 74 q^{41} - 116 q^{42} + 52 q^{43} + 17 q^{44} - 126 q^{45} + 8 q^{46} + 64 q^{47} - 3 q^{48} + 85 q^{49} - q^{50} + 104 q^{51} + 25 q^{52} + 102 q^{53} + 89 q^{54} + 182 q^{55} + 24 q^{56} + 78 q^{57} + 178 q^{58} + 132 q^{59} + 70 q^{60} + 170 q^{61} + 168 q^{62} + 124 q^{63} + 9 q^{64} + 162 q^{65} + 145 q^{66} + 204 q^{67} + 38 q^{68} + 84 q^{69} + 160 q^{70} + 40 q^{71} + 85 q^{72} + 98 q^{73} + 122 q^{74} + 53 q^{75} + 92 q^{76} + 120 q^{77} + 133 q^{78} + 168 q^{79} + 34 q^{80} + 37 q^{81} + 98 q^{82} + 12 q^{83} + 32 q^{84} + 96 q^{85} + 84 q^{86} - 42 q^{87} + 17 q^{88} + 90 q^{89} + 10 q^{90} - 48 q^{91} + 24 q^{92} + 44 q^{93} + 16 q^{94} - 48 q^{95} - 3 q^{96} + 54 q^{97} - 75 q^{98} - 119 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(858))\)

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
858.2.a \(\chi_{858}(1, \cdot)\) 858.2.a.a 1 1
858.2.a.b 1
858.2.a.c 1
858.2.a.d 1
858.2.a.e 1
858.2.a.f 1
858.2.a.g 1
858.2.a.h 1
858.2.a.i 1
858.2.a.j 1
858.2.a.k 1
858.2.a.l 1
858.2.a.m 1
858.2.a.n 2
858.2.a.o 2
858.2.a.p 2
858.2.a.q 2
858.2.b \(\chi_{858}(131, \cdot)\) 858.2.b.a 4 1
858.2.b.b 4
858.2.b.c 4
858.2.b.d 4
858.2.b.e 4
858.2.b.f 4
858.2.b.g 12
858.2.b.h 12
858.2.c \(\chi_{858}(727, \cdot)\) 858.2.c.a 2 1
858.2.c.b 2
858.2.c.c 4
858.2.c.d 8
858.2.c.e 8
858.2.h \(\chi_{858}(857, \cdot)\) 858.2.h.a 8 1
858.2.h.b 12
858.2.h.c 12
858.2.h.d 24
858.2.i \(\chi_{858}(133, \cdot)\) 858.2.i.a 2 2
858.2.i.b 2
858.2.i.c 2
858.2.i.d 2
858.2.i.e 2
858.2.i.f 2
858.2.i.g 2
858.2.i.h 2
858.2.i.i 4
858.2.i.j 4
858.2.i.k 4
858.2.i.l 6
858.2.i.m 6
858.2.i.n 8
858.2.l \(\chi_{858}(109, \cdot)\) 858.2.l.a 4 2
858.2.l.b 12
858.2.l.c 16
858.2.l.d 24
858.2.m \(\chi_{858}(551, \cdot)\) 858.2.m.a 4 2
858.2.m.b 40
858.2.m.c 44
858.2.n \(\chi_{858}(157, \cdot)\) 858.2.n.a 4 4
858.2.n.b 4
858.2.n.c 4
858.2.n.d 4
858.2.n.e 4
858.2.n.f 4
858.2.n.g 4
858.2.n.h 8
858.2.n.i 8
858.2.n.j 12
858.2.n.k 12
858.2.n.l 12
858.2.n.m 16
858.2.q \(\chi_{858}(199, \cdot)\) 858.2.q.a 4 2
858.2.q.b 4
858.2.q.c 8
858.2.q.d 12
858.2.q.e 12
858.2.r \(\chi_{858}(263, \cdot)\) 858.2.r.a 56 2
858.2.r.b 56
858.2.s \(\chi_{858}(329, \cdot)\) 858.2.s.a 112 2
858.2.v \(\chi_{858}(233, \cdot)\) 858.2.v.a 224 4
858.2.ba \(\chi_{858}(365, \cdot)\) 858.2.ba.a 96 4
858.2.ba.b 96
858.2.bb \(\chi_{858}(25, \cdot)\) 858.2.bb.a 56 4
858.2.bb.b 56
858.2.bc \(\chi_{858}(89, \cdot)\) 858.2.bc.a 8 4
858.2.bc.b 8
858.2.bc.c 80
858.2.bc.d 96
858.2.bd \(\chi_{858}(175, \cdot)\) 858.2.bd.a 8 4
858.2.bd.b 48
858.2.bd.c 56
858.2.bg \(\chi_{858}(289, \cdot)\) 858.2.bg.a 56 8
858.2.bg.b 56
858.2.bg.c 56
858.2.bg.d 56
858.2.bh \(\chi_{858}(73, \cdot)\) 858.2.bh.a 112 8
858.2.bh.b 112
858.2.bi \(\chi_{858}(5, \cdot)\) 858.2.bi.a 448 8
858.2.bn \(\chi_{858}(17, \cdot)\) 858.2.bn.a 448 8
858.2.bo \(\chi_{858}(49, \cdot)\) 858.2.bo.a 112 8
858.2.bo.b 112
858.2.bp \(\chi_{858}(29, \cdot)\) 858.2.bp.a 224 8
858.2.bp.b 224
858.2.bu \(\chi_{858}(59, \cdot)\) 858.2.bu.a 896 16
858.2.bv \(\chi_{858}(7, \cdot)\) 858.2.bv.a 224 16
858.2.bv.b 224

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(858))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(858)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 2}\)