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Properties

Label 468.2
Level 468
Weight 2
Dimension 2659
Nonzero newspaces 30
Newform subspaces 81
Sturm bound 24192
Trace bound 15

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Defining parameters

Level: \( N \) = \( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Newform subspaces: \( 81 \)
Sturm bound: \(24192\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(468))\).

Total New Old
Modular forms 6528 2859 3669
Cusp forms 5569 2659 2910
Eisenstein series 959 200 759

Trace form

\( 2659 q - 12 q^{2} - 8 q^{4} - 18 q^{5} - 18 q^{6} + 4 q^{7} - 18 q^{8} - 24 q^{9} + O(q^{10}) \) \( 2659 q - 12 q^{2} - 8 q^{4} - 18 q^{5} - 18 q^{6} + 4 q^{7} - 18 q^{8} - 24 q^{9} - 46 q^{10} - 36 q^{12} - 41 q^{13} - 60 q^{14} - 18 q^{15} - 32 q^{16} - 63 q^{17} - 60 q^{18} + 4 q^{19} - 30 q^{20} - 42 q^{21} + 6 q^{22} + 6 q^{23} - 30 q^{24} + 9 q^{25} + 12 q^{26} + 9 q^{29} + 12 q^{30} + 72 q^{31} + 78 q^{32} - 42 q^{33} + 32 q^{34} + 114 q^{35} + 42 q^{36} - 43 q^{37} + 18 q^{38} + 51 q^{39} - 64 q^{40} + 27 q^{41} + 12 q^{42} + 40 q^{43} - 48 q^{44} - 18 q^{45} - 138 q^{46} + 48 q^{47} - 66 q^{48} + 44 q^{49} - 150 q^{50} + 24 q^{51} - 104 q^{52} - 24 q^{53} - 102 q^{54} - 30 q^{55} - 108 q^{56} - 60 q^{57} - 130 q^{58} - 12 q^{59} - 96 q^{60} - 13 q^{61} - 102 q^{62} - 42 q^{63} - 212 q^{64} - 108 q^{65} - 120 q^{66} - 74 q^{67} - 222 q^{68} - 42 q^{69} - 252 q^{70} - 108 q^{71} - 138 q^{72} - 156 q^{73} - 210 q^{74} - 96 q^{75} - 192 q^{76} - 198 q^{77} - 240 q^{78} - 78 q^{79} - 360 q^{80} - 120 q^{81} - 262 q^{82} - 216 q^{83} - 252 q^{84} - 239 q^{85} - 318 q^{86} - 78 q^{87} - 222 q^{88} - 204 q^{89} - 192 q^{90} - 92 q^{91} - 300 q^{92} - 210 q^{93} - 138 q^{94} - 120 q^{95} - 84 q^{96} - 118 q^{97} - 198 q^{98} - 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(468))\)

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
468.2.a \(\chi_{468}(1, \cdot)\) 468.2.a.a 1 1
468.2.a.b 1
468.2.a.c 1
468.2.a.d 1
468.2.a.e 1
468.2.b \(\chi_{468}(181, \cdot)\) 468.2.b.a 2 1
468.2.b.b 2
468.2.b.c 2
468.2.c \(\chi_{468}(287, \cdot)\) 468.2.c.a 4 1
468.2.c.b 8
468.2.c.c 12
468.2.h \(\chi_{468}(467, \cdot)\) 468.2.h.a 4 1
468.2.h.b 4
468.2.h.c 4
468.2.h.d 16
468.2.i \(\chi_{468}(157, \cdot)\) 468.2.i.a 2 2
468.2.i.b 10
468.2.i.c 12
468.2.j \(\chi_{468}(133, \cdot)\) 468.2.j.a 28 2
468.2.k \(\chi_{468}(61, \cdot)\) 468.2.k.a 28 2
468.2.l \(\chi_{468}(217, \cdot)\) 468.2.l.a 2 2
468.2.l.b 2
468.2.l.c 2
468.2.l.d 2
468.2.l.e 4
468.2.n \(\chi_{468}(307, \cdot)\) 468.2.n.a 2 2
468.2.n.b 2
468.2.n.c 2
468.2.n.d 2
468.2.n.e 2
468.2.n.f 2
468.2.n.g 2
468.2.n.h 8
468.2.n.i 8
468.2.n.j 10
468.2.n.k 10
468.2.n.l 16
468.2.p \(\chi_{468}(125, \cdot)\) 468.2.p.a 12 2
468.2.s \(\chi_{468}(35, \cdot)\) 468.2.s.a 4 2
468.2.s.b 4
468.2.s.c 8
468.2.s.d 40
468.2.t \(\chi_{468}(361, \cdot)\) 468.2.t.a 2 2
468.2.t.b 2
468.2.t.c 2
468.2.t.d 4
468.2.w \(\chi_{468}(95, \cdot)\) 468.2.w.a 160 2
468.2.x \(\chi_{468}(155, \cdot)\) 468.2.x.a 160 2
468.2.bc \(\chi_{468}(23, \cdot)\) 468.2.bc.a 160 2
468.2.bd \(\chi_{468}(191, \cdot)\) 468.2.bd.a 160 2
468.2.be \(\chi_{468}(49, \cdot)\) 468.2.be.a 2 2
468.2.be.b 6
468.2.be.c 20
468.2.bj \(\chi_{468}(121, \cdot)\) 468.2.bj.a 2 2
468.2.bj.b 6
468.2.bj.c 20
468.2.bk \(\chi_{468}(131, \cdot)\) 468.2.bk.a 72 2
468.2.bk.b 72
468.2.bl \(\chi_{468}(25, \cdot)\) 468.2.bl.a 4 2
468.2.bl.b 24
468.2.bm \(\chi_{468}(263, \cdot)\) 468.2.bm.a 160 2
468.2.bp \(\chi_{468}(179, \cdot)\) 468.2.bp.a 4 2
468.2.bp.b 4
468.2.bp.c 8
468.2.bp.d 40
468.2.bs \(\chi_{468}(31, \cdot)\) 468.2.bs.a 320 4
468.2.bv \(\chi_{468}(89, \cdot)\) 468.2.bv.a 16 4
468.2.bw \(\chi_{468}(149, \cdot)\) 468.2.bw.a 56 4
468.2.bz \(\chi_{468}(41, \cdot)\) 468.2.bz.a 56 4
468.2.cb \(\chi_{468}(19, \cdot)\) 468.2.cb.a 4 4
468.2.cb.b 4
468.2.cb.c 4
468.2.cb.d 4
468.2.cb.e 4
468.2.cb.f 16
468.2.cb.g 24
468.2.cb.h 24
468.2.cb.i 48
468.2.cc \(\chi_{468}(115, \cdot)\) 468.2.cc.a 320 4
468.2.cf \(\chi_{468}(7, \cdot)\) 468.2.cf.a 320 4
468.2.cg \(\chi_{468}(5, \cdot)\) 468.2.cg.a 56 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(468))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(468)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 2}\)