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Properties

Label 693.6
Level 693
Weight 6
Dimension 64050
Nonzero newspaces 40
Sturm bound 207360
Trace bound 9

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Defining parameters

Level: \( N \) = \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(207360\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(693))\).

Total New Old
Modular forms 87360 64862 22498
Cusp forms 85440 64050 21390
Eisenstein series 1920 812 1108

Trace form

\( 64050 q - 6 q^{2} - 104 q^{3} - 350 q^{4} + 312 q^{5} + 628 q^{6} - 144 q^{7} - 3764 q^{8} - 1712 q^{9} + O(q^{10}) \) \( 64050 q - 6 q^{2} - 104 q^{3} - 350 q^{4} + 312 q^{5} + 628 q^{6} - 144 q^{7} - 3764 q^{8} - 1712 q^{9} - 1110 q^{10} + 2648 q^{11} + 10376 q^{12} + 170 q^{13} + 7182 q^{14} - 1760 q^{15} - 8750 q^{16} - 22950 q^{17} - 38408 q^{18} - 5150 q^{19} - 5534 q^{20} + 3620 q^{21} + 22284 q^{22} - 8078 q^{23} + 21340 q^{24} + 52358 q^{25} + 58534 q^{26} + 29800 q^{27} + 41138 q^{28} - 4796 q^{29} - 61460 q^{30} - 88936 q^{31} - 105236 q^{32} - 89184 q^{33} + 37252 q^{34} + 35494 q^{35} + 59612 q^{36} - 31848 q^{37} + 97474 q^{38} + 64516 q^{39} + 7382 q^{40} - 29142 q^{41} - 163108 q^{42} - 41692 q^{43} - 239276 q^{44} + 4980 q^{45} + 311474 q^{46} + 152054 q^{47} + 218588 q^{48} + 157340 q^{49} + 186112 q^{50} - 155404 q^{51} - 303374 q^{52} - 463450 q^{53} - 369720 q^{54} + 399756 q^{55} + 126810 q^{56} + 120000 q^{57} + 575570 q^{58} + 485832 q^{59} + 1249020 q^{60} - 483896 q^{61} + 51942 q^{62} + 643860 q^{63} - 1847556 q^{64} - 900948 q^{65} - 1192894 q^{66} - 1298074 q^{67} - 2036590 q^{68} - 1322064 q^{69} + 1591240 q^{70} + 942294 q^{71} + 334660 q^{72} + 1916884 q^{73} + 2448882 q^{74} + 1100612 q^{75} + 570700 q^{76} + 332382 q^{77} + 2685960 q^{78} - 1848844 q^{79} - 1270458 q^{80} + 633832 q^{81} - 5690364 q^{82} - 1930756 q^{83} - 2141830 q^{84} - 44672 q^{85} - 3065732 q^{86} - 3535332 q^{87} + 2306672 q^{88} - 1549166 q^{89} - 2956228 q^{90} + 2884148 q^{91} + 5965156 q^{92} + 3126876 q^{93} + 4291686 q^{94} + 5417184 q^{95} + 8027492 q^{96} - 304952 q^{97} + 254272 q^{98} + 2998128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(693))\)

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
693.6.a \(\chi_{693}(1, \cdot)\) 693.6.a.a 1 1
693.6.a.b 1
693.6.a.c 4
693.6.a.d 4
693.6.a.e 5
693.6.a.f 5
693.6.a.g 5
693.6.a.h 5
693.6.a.i 6
693.6.a.j 8
693.6.a.k 8
693.6.a.l 8
693.6.a.m 8
693.6.a.n 8
693.6.a.o 12
693.6.a.p 12
693.6.a.q 12
693.6.a.r 12
693.6.c \(\chi_{693}(307, \cdot)\) n/a 198 1
693.6.e \(\chi_{693}(188, \cdot)\) n/a 136 1
693.6.g \(\chi_{693}(197, \cdot)\) n/a 120 1
693.6.i \(\chi_{693}(100, \cdot)\) n/a 332 2
693.6.j \(\chi_{693}(232, \cdot)\) n/a 600 2
693.6.k \(\chi_{693}(67, \cdot)\) n/a 800 2
693.6.l \(\chi_{693}(529, \cdot)\) n/a 800 2
693.6.m \(\chi_{693}(64, \cdot)\) n/a 600 4
693.6.n \(\chi_{693}(320, \cdot)\) n/a 800 2
693.6.p \(\chi_{693}(241, \cdot)\) n/a 952 2
693.6.r \(\chi_{693}(32, \cdot)\) n/a 952 2
693.6.w \(\chi_{693}(428, \cdot)\) n/a 720 2
693.6.x \(\chi_{693}(296, \cdot)\) n/a 320 2
693.6.ba \(\chi_{693}(439, \cdot)\) n/a 952 2
693.6.bd \(\chi_{693}(419, \cdot)\) n/a 800 2
693.6.be \(\chi_{693}(89, \cdot)\) n/a 264 2
693.6.bg \(\chi_{693}(10, \cdot)\) n/a 396 2
693.6.bj \(\chi_{693}(76, \cdot)\) n/a 952 2
693.6.bk \(\chi_{693}(122, \cdot)\) n/a 800 2
693.6.bn \(\chi_{693}(263, \cdot)\) n/a 952 2
693.6.bq \(\chi_{693}(8, \cdot)\) n/a 480 4
693.6.bs \(\chi_{693}(125, \cdot)\) n/a 640 4
693.6.bu \(\chi_{693}(118, \cdot)\) n/a 792 4
693.6.bw \(\chi_{693}(25, \cdot)\) n/a 3808 8
693.6.bx \(\chi_{693}(4, \cdot)\) n/a 3808 8
693.6.by \(\chi_{693}(37, \cdot)\) n/a 1584 8
693.6.bz \(\chi_{693}(148, \cdot)\) n/a 2880 8
693.6.cb \(\chi_{693}(74, \cdot)\) n/a 3808 8
693.6.ce \(\chi_{693}(47, \cdot)\) n/a 3808 8
693.6.cg \(\chi_{693}(19, \cdot)\) n/a 1584 8
693.6.ch \(\chi_{693}(13, \cdot)\) n/a 3808 8
693.6.cj \(\chi_{693}(20, \cdot)\) n/a 3808 8
693.6.cm \(\chi_{693}(26, \cdot)\) n/a 1280 8
693.6.co \(\chi_{693}(61, \cdot)\) n/a 3808 8
693.6.cq \(\chi_{693}(29, \cdot)\) n/a 2880 8
693.6.ct \(\chi_{693}(107, \cdot)\) n/a 1280 8
693.6.cx \(\chi_{693}(2, \cdot)\) n/a 3808 8
693.6.cz \(\chi_{693}(40, \cdot)\) n/a 3808 8
693.6.db \(\chi_{693}(5, \cdot)\) n/a 3808 8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(693))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(693)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(693))\)\(^{\oplus 1}\)