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Properties

Label 546.2
Level 546
Weight 2
Dimension 1905
Nonzero newspaces 30
Newform subspaces 124
Sturm bound 32256
Trace bound 11

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Defining parameters

Level: \( N \) = \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Newform subspaces: \( 124 \)
Sturm bound: \(32256\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(546))\).

Total New Old
Modular forms 8640 1905 6735
Cusp forms 7489 1905 5584
Eisenstein series 1151 0 1151

Trace form

\( 1905 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 9 q^{6} + 25 q^{7} + 9 q^{8} + 21 q^{9} + O(q^{10}) \) \( 1905 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 9 q^{6} + 25 q^{7} + 9 q^{8} + 21 q^{9} + 66 q^{10} + 60 q^{11} + 9 q^{12} + 85 q^{13} + 9 q^{14} + 30 q^{15} + 13 q^{16} + 30 q^{17} - 15 q^{18} + 84 q^{19} - 6 q^{20} - 7 q^{21} - 36 q^{22} - 15 q^{24} + 15 q^{25} - 15 q^{26} + 73 q^{27} + 9 q^{28} + 18 q^{29} - 42 q^{30} + 32 q^{31} - 3 q^{32} - 12 q^{33} - 6 q^{34} + 30 q^{35} - 35 q^{36} + 10 q^{37} + 12 q^{38} - 87 q^{39} + 6 q^{40} - 18 q^{41} + 9 q^{42} + 92 q^{43} + 12 q^{44} - 102 q^{45} + 24 q^{46} - 24 q^{47} + q^{48} + 5 q^{49} + 15 q^{50} - 30 q^{51} - 23 q^{52} + 54 q^{53} + 33 q^{54} + 96 q^{55} + 33 q^{56} + 124 q^{57} - 6 q^{58} + 108 q^{59} + 6 q^{60} + 50 q^{61} + 96 q^{62} + 17 q^{63} + 17 q^{64} + 126 q^{65} + 60 q^{66} + 52 q^{67} - 18 q^{68} + 72 q^{69} - 18 q^{70} + 24 q^{71} + 69 q^{72} - 6 q^{73} - 30 q^{74} - 129 q^{75} - 108 q^{76} - 252 q^{77} - 27 q^{78} - 288 q^{79} + 18 q^{80} + 45 q^{81} - 354 q^{82} - 300 q^{83} - 103 q^{84} - 504 q^{85} - 204 q^{86} - 354 q^{87} - 12 q^{88} - 414 q^{89} - 90 q^{90} - 519 q^{91} - 216 q^{92} - 272 q^{93} - 480 q^{94} - 528 q^{95} - 15 q^{96} - 670 q^{97} - 291 q^{98} - 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(546))\)

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
546.2.a \(\chi_{546}(1, \cdot)\) 546.2.a.a 1 1
546.2.a.b 1
546.2.a.c 1
546.2.a.d 1
546.2.a.e 1
546.2.a.f 1
546.2.a.g 1
546.2.a.h 2
546.2.a.i 2
546.2.a.j 2
546.2.c \(\chi_{546}(337, \cdot)\) 546.2.c.a 2 1
546.2.c.b 2
546.2.c.c 2
546.2.c.d 2
546.2.c.e 4
546.2.e \(\chi_{546}(545, \cdot)\) 546.2.e.a 2 1
546.2.e.b 2
546.2.e.c 2
546.2.e.d 2
546.2.e.e 8
546.2.e.f 8
546.2.e.g 8
546.2.e.h 8
546.2.g \(\chi_{546}(209, \cdot)\) 546.2.g.a 4 1
546.2.g.b 4
546.2.g.c 12
546.2.g.d 12
546.2.i \(\chi_{546}(79, \cdot)\) 546.2.i.a 2 2
546.2.i.b 2
546.2.i.c 2
546.2.i.d 2
546.2.i.e 2
546.2.i.f 2
546.2.i.g 2
546.2.i.h 4
546.2.i.i 4
546.2.i.j 4
546.2.i.k 6
546.2.j \(\chi_{546}(289, \cdot)\) 546.2.j.a 2 2
546.2.j.b 8
546.2.j.c 8
546.2.j.d 8
546.2.j.e 10
546.2.k \(\chi_{546}(373, \cdot)\) 546.2.k.a 2 2
546.2.k.b 8
546.2.k.c 8
546.2.k.d 8
546.2.k.e 10
546.2.l \(\chi_{546}(211, \cdot)\) 546.2.l.a 2 2
546.2.l.b 2
546.2.l.c 2
546.2.l.d 2
546.2.l.e 2
546.2.l.f 2
546.2.l.g 2
546.2.l.h 2
546.2.l.i 4
546.2.l.j 4
546.2.l.k 4
546.2.l.l 4
546.2.o \(\chi_{546}(265, \cdot)\) 546.2.o.a 8 2
546.2.o.b 8
546.2.o.c 8
546.2.o.d 8
546.2.p \(\chi_{546}(239, \cdot)\) 546.2.p.a 8 2
546.2.p.b 8
546.2.p.c 20
546.2.p.d 20
546.2.q \(\chi_{546}(251, \cdot)\) 546.2.q.a 2 2
546.2.q.b 2
546.2.q.c 2
546.2.q.d 2
546.2.q.e 4
546.2.q.f 4
546.2.q.g 4
546.2.q.h 4
546.2.q.i 24
546.2.q.j 24
546.2.s \(\chi_{546}(43, \cdot)\) 546.2.s.a 4 2
546.2.s.b 4
546.2.s.c 4
546.2.s.d 4
546.2.s.e 8
546.2.u \(\chi_{546}(185, \cdot)\) 546.2.u.a 76 2
546.2.z \(\chi_{546}(131, \cdot)\) 546.2.z.a 32 2
546.2.z.b 32
546.2.bb \(\chi_{546}(269, \cdot)\) 546.2.bb.a 76 2
546.2.bd \(\chi_{546}(121, \cdot)\) 546.2.bd.a 16 2
546.2.bd.b 20
546.2.bg \(\chi_{546}(311, \cdot)\) 546.2.bg.a 36 2
546.2.bg.b 36
546.2.bi \(\chi_{546}(17, \cdot)\) 546.2.bi.a 2 2
546.2.bi.b 2
546.2.bi.c 2
546.2.bi.d 2
546.2.bi.e 34
546.2.bi.f 34
546.2.bk \(\chi_{546}(25, \cdot)\) 546.2.bk.a 8 2
546.2.bk.b 12
546.2.bk.c 20
546.2.bm \(\chi_{546}(205, \cdot)\) 546.2.bm.a 16 2
546.2.bm.b 20
546.2.bn \(\chi_{546}(101, \cdot)\) 546.2.bn.a 2 2
546.2.bn.b 2
546.2.bn.c 2
546.2.bn.d 2
546.2.bn.e 34
546.2.bn.f 34
546.2.bq \(\chi_{546}(419, \cdot)\) 546.2.bq.a 4 2
546.2.bq.b 4
546.2.bq.c 64
546.2.bu \(\chi_{546}(71, \cdot)\) 546.2.bu.a 56 4
546.2.bu.b 56
546.2.bv \(\chi_{546}(317, \cdot)\) 546.2.bv.a 144 4
546.2.bw \(\chi_{546}(11, \cdot)\) 546.2.bw.a 152 4
546.2.bx \(\chi_{546}(97, \cdot)\) 546.2.bx.a 40 4
546.2.bx.b 40
546.2.by \(\chi_{546}(19, \cdot)\) 546.2.by.a 32 4
546.2.by.b 40
546.2.bz \(\chi_{546}(31, \cdot)\) 546.2.bz.a 40 4
546.2.bz.b 40
546.2.cg \(\chi_{546}(145, \cdot)\) 546.2.cg.a 32 4
546.2.cg.b 40
546.2.ch \(\chi_{546}(137, \cdot)\) 546.2.ch.a 152 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(546))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(546)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(546))\)\(^{\oplus 1}\)