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Properties

Label 726.4
Level 726
Weight 4
Dimension 10711
Nonzero newspaces 8
Sturm bound 116160
Trace bound 1

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Defining parameters

Level: \( N \) = \( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(116160\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(726))\).

Total New Old
Modular forms 44200 10711 33489
Cusp forms 42920 10711 32209
Eisenstein series 1280 0 1280

Trace form

\( 10711 q - 2 q^{2} - 3 q^{3} + 4 q^{4} + 6 q^{5} + 106 q^{6} + 64 q^{7} - 8 q^{8} - 311 q^{9} + O(q^{10}) \) \( 10711 q - 2 q^{2} - 3 q^{3} + 4 q^{4} + 6 q^{5} + 106 q^{6} + 64 q^{7} - 8 q^{8} - 311 q^{9} - 412 q^{10} - 200 q^{11} - 172 q^{12} - 122 q^{13} + 112 q^{14} + 802 q^{15} + 16 q^{16} + 1114 q^{17} + 442 q^{18} - 880 q^{19} + 24 q^{20} - 792 q^{21} - 592 q^{23} - 376 q^{24} - 809 q^{25} - 76 q^{26} + 93 q^{27} - 64 q^{28} + 1430 q^{29} + 1596 q^{30} + 2672 q^{31} - 32 q^{32} + 1935 q^{33} + 252 q^{34} + 1064 q^{35} + 236 q^{36} + 254 q^{37} - 40 q^{38} - 1634 q^{39} - 48 q^{40} - 1438 q^{41} - 376 q^{42} + 4468 q^{43} + 1120 q^{44} - 3246 q^{45} + 1104 q^{46} - 1096 q^{47} - 48 q^{48} - 5407 q^{49} - 2542 q^{50} - 3912 q^{51} - 3688 q^{52} - 6042 q^{53} - 1026 q^{54} - 2540 q^{55} + 128 q^{56} - 3070 q^{57} - 6780 q^{58} - 4740 q^{59} - 1032 q^{60} + 4102 q^{61} + 5696 q^{62} + 11656 q^{63} + 64 q^{64} + 13668 q^{65} + 2920 q^{66} + 14244 q^{67} + 4456 q^{68} + 7976 q^{69} + 3552 q^{70} - 6568 q^{71} - 2312 q^{72} - 2542 q^{73} - 6108 q^{74} - 13323 q^{75} - 2960 q^{76} - 4100 q^{77} - 5692 q^{78} - 8920 q^{79} - 2464 q^{80} - 24199 q^{81} - 14204 q^{82} - 4572 q^{83} - 5088 q^{84} - 17956 q^{85} + 1784 q^{86} - 90 q^{87} + 1120 q^{88} + 3810 q^{89} + 10972 q^{90} + 34872 q^{91} + 672 q^{92} + 26324 q^{93} + 18752 q^{94} + 18840 q^{95} + 96 q^{96} + 18494 q^{97} + 174 q^{98} + 7890 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(726))\)

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
726.4.a \(\chi_{726}(1, \cdot)\) 726.4.a.a 1 1
726.4.a.b 1
726.4.a.c 1
726.4.a.d 1
726.4.a.e 1
726.4.a.f 1
726.4.a.g 1
726.4.a.h 1
726.4.a.i 1
726.4.a.j 2
726.4.a.k 2
726.4.a.l 2
726.4.a.m 2
726.4.a.n 2
726.4.a.o 2
726.4.a.p 2
726.4.a.q 2
726.4.a.r 2
726.4.a.s 2
726.4.a.t 2
726.4.a.u 4
726.4.a.v 4
726.4.a.w 4
726.4.a.x 4
726.4.a.y 4
726.4.a.z 4
726.4.b \(\chi_{726}(725, \cdot)\) n/a 108 1
726.4.e \(\chi_{726}(487, \cdot)\) n/a 216 4
726.4.h \(\chi_{726}(161, \cdot)\) n/a 432 4
726.4.i \(\chi_{726}(67, \cdot)\) n/a 660 10
726.4.l \(\chi_{726}(65, \cdot)\) n/a 1320 10
726.4.m \(\chi_{726}(25, \cdot)\) n/a 2640 40
726.4.n \(\chi_{726}(17, \cdot)\) n/a 5280 40

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(726))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(726)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)