Properties

Label 726.6
Level 726
Weight 6
Dimension 17851
Nonzero newspaces 8
Sturm bound 174240
Trace bound 1

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Defining parameters

Level: \( N \) = \( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(174240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(726))\).

Total New Old
Modular forms 73240 17851 55389
Cusp forms 71960 17851 54109
Eisenstein series 1280 0 1280

Trace form

\( 17851 q + 4 q^{2} - 9 q^{3} + 16 q^{4} - 66 q^{5} + 4 q^{6} - 2184 q^{7} + 64 q^{8} + 2281 q^{9} + O(q^{10}) \) \( 17851 q + 4 q^{2} - 9 q^{3} + 16 q^{4} - 66 q^{5} + 4 q^{6} - 2184 q^{7} + 64 q^{8} + 2281 q^{9} + 3736 q^{10} + 1780 q^{11} + 176 q^{12} - 4698 q^{13} - 8096 q^{14} - 12386 q^{15} + 256 q^{16} - 3614 q^{17} + 9964 q^{18} + 9896 q^{19} - 1056 q^{20} + 16056 q^{21} + 11360 q^{23} - 1216 q^{24} - 24289 q^{25} - 2632 q^{26} + 39531 q^{27} + 2816 q^{28} - 19666 q^{29} - 30984 q^{30} + 62848 q^{31} + 1024 q^{32} - 43605 q^{33} - 1656 q^{34} - 67576 q^{35} + 3056 q^{36} - 8458 q^{37} + 3824 q^{38} + 110782 q^{39} - 4224 q^{40} + 67394 q^{41} + 114224 q^{42} + 157756 q^{43} - 25280 q^{44} - 130746 q^{45} - 207200 q^{46} - 287200 q^{47} - 2304 q^{48} - 179431 q^{49} + 33404 q^{50} - 125964 q^{51} + 157152 q^{52} + 286854 q^{53} + 55404 q^{54} + 228900 q^{55} + 11264 q^{56} + 504086 q^{57} + 156056 q^{58} - 11940 q^{59} - 53856 q^{60} + 40550 q^{61} - 99328 q^{62} - 399884 q^{63} + 4096 q^{64} - 1091532 q^{65} - 286160 q^{66} - 545564 q^{67} - 57824 q^{68} - 87460 q^{69} + 456896 q^{70} + 60680 q^{71} + 84544 q^{72} + 419962 q^{73} + 334488 q^{74} + 1334331 q^{75} + 246336 q^{76} + 198520 q^{77} + 436808 q^{78} + 577088 q^{79} + 95744 q^{80} - 1005439 q^{81} - 547144 q^{82} - 355788 q^{83} - 67584 q^{84} + 303044 q^{85} - 955216 q^{86} - 50166 q^{87} - 190720 q^{88} - 449262 q^{89} - 25304 q^{90} + 1220912 q^{91} + 9600 q^{92} + 656468 q^{93} + 269440 q^{94} + 721824 q^{95} - 9216 q^{96} - 2920738 q^{97} + 56676 q^{98} - 1255350 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(726))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
726.6.a \(\chi_{726}(1, \cdot)\) 726.6.a.a 1 1
726.6.a.b 1
726.6.a.c 1
726.6.a.d 1
726.6.a.e 1
726.6.a.f 1
726.6.a.g 1
726.6.a.h 1
726.6.a.i 1
726.6.a.j 1
726.6.a.k 1
726.6.a.l 2
726.6.a.m 2
726.6.a.n 2
726.6.a.o 2
726.6.a.p 2
726.6.a.q 2
726.6.a.r 2
726.6.a.s 2
726.6.a.t 2
726.6.a.u 2
726.6.a.v 3
726.6.a.w 3
726.6.a.x 3
726.6.a.y 3
726.6.a.z 4
726.6.a.ba 4
726.6.a.bb 4
726.6.a.bc 4
726.6.a.bd 4
726.6.a.be 4
726.6.a.bf 6
726.6.a.bg 6
726.6.a.bh 6
726.6.a.bi 6
726.6.b \(\chi_{726}(725, \cdot)\) n/a 180 1
726.6.e \(\chi_{726}(487, \cdot)\) n/a 360 4
726.6.h \(\chi_{726}(161, \cdot)\) n/a 720 4
726.6.i \(\chi_{726}(67, \cdot)\) n/a 1100 10
726.6.l \(\chi_{726}(65, \cdot)\) n/a 2200 10
726.6.m \(\chi_{726}(25, \cdot)\) n/a 4400 40
726.6.n \(\chi_{726}(17, \cdot)\) n/a 8800 40

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(726))\) into lower level spaces

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