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Properties

Label 546.6
Level 546
Weight 6
Dimension 9544
Nonzero newspaces 30
Sturm bound 96768
Trace bound 7

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Defining parameters

Level: \( N \) = \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(96768\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(546))\).

Total New Old
Modular forms 40896 9544 31352
Cusp forms 39744 9544 30200
Eisenstein series 1152 0 1152

Trace form

\( 9544 q + 16 q^{2} - 64 q^{4} + 288 q^{6} + 2472 q^{7} - 512 q^{8} - 1788 q^{9} + O(q^{10}) \) \( 9544 q + 16 q^{2} - 64 q^{4} + 288 q^{6} + 2472 q^{7} - 512 q^{8} - 1788 q^{9} - 4272 q^{10} + 2256 q^{11} + 1152 q^{12} + 15924 q^{13} + 2464 q^{14} + 5688 q^{15} - 3072 q^{16} - 12036 q^{17} - 5568 q^{18} - 20128 q^{19} + 3648 q^{20} - 12744 q^{21} - 960 q^{22} + 7656 q^{23} + 1536 q^{24} + 77272 q^{25} - 7904 q^{26} + 30312 q^{27} - 17024 q^{28} - 29436 q^{29} + 13152 q^{30} - 65568 q^{31} + 4096 q^{32} + 74640 q^{33} + 48864 q^{34} + 41304 q^{35} - 67776 q^{36} + 156772 q^{37} + 10400 q^{38} - 131088 q^{39} - 64512 q^{40} - 117372 q^{41} - 127584 q^{42} - 276624 q^{43} - 32256 q^{44} + 232620 q^{45} + 194880 q^{46} + 197208 q^{47} + 40700 q^{49} + 341824 q^{50} + 345312 q^{51} + 27264 q^{52} - 165168 q^{53} - 127296 q^{54} - 376008 q^{55} - 146432 q^{56} - 535224 q^{57} - 337968 q^{58} - 481296 q^{59} - 38400 q^{60} - 458124 q^{61} + 669824 q^{62} - 58704 q^{63} + 229376 q^{64} + 729312 q^{65} + 21696 q^{66} + 855664 q^{67} - 111168 q^{68} + 558528 q^{69} + 30624 q^{70} - 28464 q^{71} - 149760 q^{72} - 640432 q^{73} - 1661488 q^{74} - 1060128 q^{75} - 44032 q^{76} + 1029144 q^{77} + 510096 q^{78} + 1957616 q^{79} + 125952 q^{80} + 1053564 q^{81} + 2069040 q^{82} + 57408 q^{83} - 89472 q^{84} - 1314132 q^{85} - 899488 q^{86} - 1857840 q^{87} - 244224 q^{88} - 3281544 q^{89} - 668736 q^{90} - 3960728 q^{91} - 1023744 q^{92} + 445800 q^{93} - 1425024 q^{94} + 653976 q^{95} + 24576 q^{96} + 446640 q^{97} + 961168 q^{98} + 788040 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(546))\)

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
546.6.a \(\chi_{546}(1, \cdot)\) 546.6.a.a 1 1
546.6.a.b 1
546.6.a.c 1
546.6.a.d 1
546.6.a.e 1
546.6.a.f 1
546.6.a.g 1
546.6.a.h 1
546.6.a.i 1
546.6.a.j 2
546.6.a.k 2
546.6.a.l 2
546.6.a.m 3
546.6.a.n 3
546.6.a.o 3
546.6.a.p 3
546.6.a.q 3
546.6.a.r 3
546.6.a.s 4
546.6.a.t 4
546.6.a.u 4
546.6.a.v 5
546.6.a.w 5
546.6.a.x 5
546.6.c \(\chi_{546}(337, \cdot)\) 546.6.c.a 16 1
546.6.c.b 16
546.6.c.c 18
546.6.c.d 18
546.6.e \(\chi_{546}(545, \cdot)\) n/a 184 1
546.6.g \(\chi_{546}(209, \cdot)\) n/a 160 1
546.6.i \(\chi_{546}(79, \cdot)\) n/a 160 2
546.6.j \(\chi_{546}(289, \cdot)\) n/a 188 2
546.6.k \(\chi_{546}(373, \cdot)\) n/a 188 2
546.6.l \(\chi_{546}(211, \cdot)\) n/a 144 2
546.6.o \(\chi_{546}(265, \cdot)\) n/a 192 2
546.6.p \(\chi_{546}(239, \cdot)\) n/a 280 2
546.6.q \(\chi_{546}(251, \cdot)\) n/a 376 2
546.6.s \(\chi_{546}(43, \cdot)\) n/a 136 2
546.6.u \(\chi_{546}(185, \cdot)\) n/a 372 2
546.6.z \(\chi_{546}(131, \cdot)\) n/a 320 2
546.6.bb \(\chi_{546}(269, \cdot)\) n/a 372 2
546.6.bd \(\chi_{546}(121, \cdot)\) n/a 188 2
546.6.bg \(\chi_{546}(311, \cdot)\) n/a 376 2
546.6.bi \(\chi_{546}(17, \cdot)\) n/a 372 2
546.6.bk \(\chi_{546}(25, \cdot)\) n/a 184 2
546.6.bm \(\chi_{546}(205, \cdot)\) n/a 188 2
546.6.bn \(\chi_{546}(101, \cdot)\) n/a 372 2
546.6.bq \(\chi_{546}(419, \cdot)\) n/a 376 2
546.6.bu \(\chi_{546}(71, \cdot)\) n/a 560 4
546.6.bv \(\chi_{546}(317, \cdot)\) n/a 752 4
546.6.bw \(\chi_{546}(11, \cdot)\) n/a 744 4
546.6.bx \(\chi_{546}(97, \cdot)\) n/a 368 4
546.6.by \(\chi_{546}(19, \cdot)\) n/a 376 4
546.6.bz \(\chi_{546}(31, \cdot)\) n/a 368 4
546.6.cg \(\chi_{546}(145, \cdot)\) n/a 376 4
546.6.ch \(\chi_{546}(137, \cdot)\) n/a 744 4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(546))\) into lower level spaces

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