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Properties

Label 546.4
Level 546
Weight 4
Dimension 5728
Nonzero newspaces 30
Sturm bound 64512
Trace bound 7

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Defining parameters

Level: \( N \) = \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(64512\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(546))\).

Total New Old
Modular forms 24768 5728 19040
Cusp forms 23616 5728 17888
Eisenstein series 1152 0 1152

Trace form

\( 5728 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 72 q^{5} - 48 q^{6} - 80 q^{7} + 64 q^{8} + 120 q^{9} + O(q^{10}) \) \( 5728 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 72 q^{5} - 48 q^{6} - 80 q^{7} + 64 q^{8} + 120 q^{9} - 264 q^{10} - 264 q^{11} - 48 q^{12} - 1088 q^{13} - 176 q^{14} - 864 q^{15} + 64 q^{16} + 420 q^{17} + 480 q^{18} + 3584 q^{19} + 624 q^{20} + 1512 q^{21} - 96 q^{22} - 408 q^{23} + 192 q^{24} - 1016 q^{25} + 304 q^{26} - 1872 q^{27} + 64 q^{28} - 852 q^{29} - 2832 q^{30} - 1648 q^{31} - 128 q^{32} - 708 q^{33} - 624 q^{34} - 384 q^{35} + 48 q^{36} + 3476 q^{37} + 272 q^{38} + 5268 q^{39} + 384 q^{40} + 1644 q^{41} + 1392 q^{42} + 944 q^{43} + 864 q^{44} + 3552 q^{45} - 2016 q^{46} - 1152 q^{47} - 384 q^{48} - 9020 q^{49} - 1952 q^{50} - 7236 q^{51} + 688 q^{52} + 2448 q^{53} + 3168 q^{54} + 3384 q^{55} + 640 q^{56} + 2328 q^{57} + 2424 q^{58} - 2352 q^{59} + 624 q^{60} + 10556 q^{61} - 1216 q^{62} + 984 q^{63} + 1024 q^{64} - 9588 q^{65} - 1632 q^{66} - 5920 q^{67} - 2736 q^{68} - 12360 q^{69} - 4080 q^{70} - 6576 q^{71} - 2016 q^{72} - 16696 q^{73} - 15688 q^{74} - 11712 q^{75} - 12640 q^{76} - 26664 q^{77} - 504 q^{78} - 8224 q^{79} + 960 q^{80} + 16296 q^{81} + 5544 q^{82} + 13776 q^{83} + 5280 q^{84} + 39252 q^{85} + 11504 q^{86} + 16032 q^{87} + 960 q^{88} + 36360 q^{89} + 6048 q^{90} + 45016 q^{91} + 15360 q^{92} + 2676 q^{93} + 34368 q^{94} + 18288 q^{95} + 768 q^{96} + 5888 q^{97} + 8248 q^{98} - 12744 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(546))\)

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
546.4.a \(\chi_{546}(1, \cdot)\) 546.4.a.a 1 1
546.4.a.b 1
546.4.a.c 1
546.4.a.d 1
546.4.a.e 1
546.4.a.f 2
546.4.a.g 2
546.4.a.h 2
546.4.a.i 2
546.4.a.j 2
546.4.a.k 2
546.4.a.l 3
546.4.a.m 3
546.4.a.n 3
546.4.a.o 3
546.4.a.p 3
546.4.a.q 4
546.4.c \(\chi_{546}(337, \cdot)\) 546.4.c.a 10 1
546.4.c.b 10
546.4.c.c 12
546.4.c.d 12
546.4.e \(\chi_{546}(545, \cdot)\) n/a 112 1
546.4.g \(\chi_{546}(209, \cdot)\) 546.4.g.a 48 1
546.4.g.b 48
546.4.i \(\chi_{546}(79, \cdot)\) 546.4.i.a 4 2
546.4.i.b 8
546.4.i.c 10
546.4.i.d 10
546.4.i.e 12
546.4.i.f 12
546.4.i.g 12
546.4.i.h 14
546.4.i.i 14
546.4.j \(\chi_{546}(289, \cdot)\) n/a 112 2
546.4.k \(\chi_{546}(373, \cdot)\) n/a 112 2
546.4.l \(\chi_{546}(211, \cdot)\) 546.4.l.a 2 2
546.4.l.b 2
546.4.l.c 8
546.4.l.d 8
546.4.l.e 10
546.4.l.f 10
546.4.l.g 10
546.4.l.h 10
546.4.l.i 10
546.4.l.j 10
546.4.o \(\chi_{546}(265, \cdot)\) n/a 112 2
546.4.p \(\chi_{546}(239, \cdot)\) n/a 168 2
546.4.q \(\chi_{546}(251, \cdot)\) n/a 224 2
546.4.s \(\chi_{546}(43, \cdot)\) 546.4.s.a 20 2
546.4.s.b 20
546.4.s.c 24
546.4.s.d 24
546.4.u \(\chi_{546}(185, \cdot)\) n/a 224 2
546.4.z \(\chi_{546}(131, \cdot)\) n/a 192 2
546.4.bb \(\chi_{546}(269, \cdot)\) n/a 224 2
546.4.bd \(\chi_{546}(121, \cdot)\) n/a 112 2
546.4.bg \(\chi_{546}(311, \cdot)\) n/a 224 2
546.4.bi \(\chi_{546}(17, \cdot)\) n/a 224 2
546.4.bk \(\chi_{546}(25, \cdot)\) n/a 112 2
546.4.bm \(\chi_{546}(205, \cdot)\) n/a 112 2
546.4.bn \(\chi_{546}(101, \cdot)\) n/a 224 2
546.4.bq \(\chi_{546}(419, \cdot)\) n/a 224 2
546.4.bu \(\chi_{546}(71, \cdot)\) n/a 336 4
546.4.bv \(\chi_{546}(317, \cdot)\) n/a 448 4
546.4.bw \(\chi_{546}(11, \cdot)\) n/a 448 4
546.4.bx \(\chi_{546}(97, \cdot)\) n/a 224 4
546.4.by \(\chi_{546}(19, \cdot)\) n/a 224 4
546.4.bz \(\chi_{546}(31, \cdot)\) n/a 224 4
546.4.cg \(\chi_{546}(145, \cdot)\) n/a 224 4
546.4.ch \(\chi_{546}(137, \cdot)\) n/a 448 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(546))\) into lower level spaces

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