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Properties

Label 756.4
Level 756
Weight 4
Dimension 20448
Nonzero newspaces 32
Sturm bound 124416
Trace bound 21

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Defining parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(124416\)
Trace bound: \(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(756))\).

Total New Old
Modular forms 47556 20768 26788
Cusp forms 45756 20448 25308
Eisenstein series 1800 320 1480

Trace form

\( 20448 q - 18 q^{2} - 16 q^{4} - 48 q^{5} - 24 q^{6} + 28 q^{7} - 30 q^{8} + 48 q^{9} + O(q^{10}) \) \( 20448 q - 18 q^{2} - 16 q^{4} - 48 q^{5} - 24 q^{6} + 28 q^{7} - 30 q^{8} + 48 q^{9} - 128 q^{10} + 276 q^{11} + 210 q^{12} - 108 q^{13} - 171 q^{14} - 468 q^{15} - 304 q^{16} - 720 q^{17} - 738 q^{18} - 88 q^{19} - 936 q^{20} - 48 q^{21} - 474 q^{22} + 480 q^{23} + 564 q^{24} + 1690 q^{25} + 24 q^{26} - 54 q^{27} - 90 q^{28} - 96 q^{29} + 378 q^{30} + 464 q^{31} + 4212 q^{32} - 1914 q^{33} + 2308 q^{34} - 1074 q^{35} + 2040 q^{36} - 2244 q^{37} + 1818 q^{38} - 132 q^{39} - 932 q^{40} - 2532 q^{41} - 2610 q^{42} + 2048 q^{43} - 7644 q^{44} + 1884 q^{45} - 3504 q^{46} + 3744 q^{47} + 834 q^{48} + 108 q^{49} + 3516 q^{50} + 6516 q^{51} - 1892 q^{52} + 4056 q^{53} + 8880 q^{54} - 720 q^{55} + 1953 q^{56} - 1230 q^{57} - 4952 q^{58} - 4158 q^{59} - 1968 q^{60} + 516 q^{61} - 3798 q^{62} - 7842 q^{63} + 242 q^{64} - 5484 q^{65} - 6222 q^{66} + 5324 q^{67} + 534 q^{68} - 1680 q^{69} + 1539 q^{70} + 3432 q^{71} + 9012 q^{72} + 7296 q^{73} + 22902 q^{74} + 6996 q^{75} + 12144 q^{76} + 9942 q^{77} + 5880 q^{78} - 3856 q^{79} + 8070 q^{80} - 7656 q^{81} + 412 q^{82} - 13140 q^{83} - 6360 q^{84} - 16036 q^{85} - 24966 q^{86} - 9648 q^{87} - 16008 q^{88} - 29454 q^{89} + 2172 q^{90} - 4906 q^{91} - 10062 q^{92} - 17208 q^{93} - 14688 q^{94} + 1368 q^{95} - 1200 q^{96} + 10176 q^{97} - 11304 q^{98} + 10152 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(756))\)

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
756.4.a \(\chi_{756}(1, \cdot)\) 756.4.a.a 1 1
756.4.a.b 1
756.4.a.c 1
756.4.a.d 1
756.4.a.e 2
756.4.a.f 2
756.4.a.g 2
756.4.a.h 2
756.4.a.i 2
756.4.a.j 2
756.4.a.k 4
756.4.a.l 4
756.4.b \(\chi_{756}(55, \cdot)\) n/a 192 1
756.4.e \(\chi_{756}(323, \cdot)\) n/a 144 1
756.4.f \(\chi_{756}(377, \cdot)\) 756.4.f.a 2 1
756.4.f.b 2
756.4.f.c 4
756.4.f.d 8
756.4.f.e 16
756.4.i \(\chi_{756}(37, \cdot)\) 756.4.i.a 48 2
756.4.j \(\chi_{756}(253, \cdot)\) 756.4.j.a 18 2
756.4.j.b 18
756.4.k \(\chi_{756}(109, \cdot)\) 756.4.k.a 2 2
756.4.k.b 2
756.4.k.c 4
756.4.k.d 4
756.4.k.e 4
756.4.k.f 16
756.4.k.g 16
756.4.k.h 16
756.4.l \(\chi_{756}(289, \cdot)\) 756.4.l.a 48 2
756.4.n \(\chi_{756}(19, \cdot)\) n/a 280 2
756.4.o \(\chi_{756}(179, \cdot)\) n/a 280 2
756.4.t \(\chi_{756}(269, \cdot)\) 756.4.t.a 2 2
756.4.t.b 2
756.4.t.c 12
756.4.t.d 16
756.4.t.e 32
756.4.w \(\chi_{756}(341, \cdot)\) 756.4.w.a 48 2
756.4.x \(\chi_{756}(125, \cdot)\) 756.4.x.a 48 2
756.4.ba \(\chi_{756}(71, \cdot)\) n/a 216 2
756.4.bb \(\chi_{756}(611, \cdot)\) n/a 280 2
756.4.be \(\chi_{756}(107, \cdot)\) n/a 384 2
756.4.bf \(\chi_{756}(271, \cdot)\) n/a 384 2
756.4.bi \(\chi_{756}(307, \cdot)\) n/a 280 2
756.4.bj \(\chi_{756}(451, \cdot)\) n/a 280 2
756.4.bm \(\chi_{756}(17, \cdot)\) 756.4.bm.a 48 2
756.4.bo \(\chi_{756}(85, \cdot)\) n/a 324 6
756.4.bp \(\chi_{756}(193, \cdot)\) n/a 432 6
756.4.bq \(\chi_{756}(25, \cdot)\) n/a 432 6
756.4.bs \(\chi_{756}(11, \cdot)\) n/a 2568 6
756.4.bt \(\chi_{756}(103, \cdot)\) n/a 2568 6
756.4.bx \(\chi_{756}(41, \cdot)\) n/a 432 6
756.4.ca \(\chi_{756}(173, \cdot)\) n/a 432 6
756.4.cc \(\chi_{756}(139, \cdot)\) n/a 2568 6
756.4.cd \(\chi_{756}(31, \cdot)\) n/a 2568 6
756.4.cf \(\chi_{756}(155, \cdot)\) n/a 1944 6
756.4.ci \(\chi_{756}(95, \cdot)\) n/a 2568 6
756.4.ck \(\chi_{756}(5, \cdot)\) n/a 432 6

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(756))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(756)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 2}\)