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Properties

Label 693.4
Level 693
Weight 4
Dimension 38270
Nonzero newspaces 40
Sturm bound 138240
Trace bound 9

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Defining parameters

Level: \( N \) = \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(138240\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(693))\).

Total New Old
Modular forms 52800 39082 13718
Cusp forms 50880 38270 12610
Eisenstein series 1920 812 1108

Trace form

\( 38270 q - 54 q^{2} - 68 q^{3} - 94 q^{4} - 126 q^{5} - 20 q^{6} - 69 q^{7} + 124 q^{8} + 124 q^{9} + O(q^{10}) \) \( 38270 q - 54 q^{2} - 68 q^{3} - 94 q^{4} - 126 q^{5} - 20 q^{6} - 69 q^{7} + 124 q^{8} + 124 q^{9} - 214 q^{10} - 283 q^{11} - 856 q^{12} - 612 q^{13} - 1086 q^{14} - 284 q^{15} + 882 q^{16} + 1470 q^{17} + 1480 q^{18} + 352 q^{19} + 2002 q^{20} + 686 q^{21} - 456 q^{22} - 1766 q^{23} - 2276 q^{24} - 2278 q^{25} - 4562 q^{26} - 2456 q^{27} - 1486 q^{28} + 70 q^{29} + 1036 q^{30} + 430 q^{31} + 3340 q^{32} + 2784 q^{33} + 2300 q^{34} + 2461 q^{35} + 3068 q^{36} + 3534 q^{37} + 8842 q^{38} + 4900 q^{39} + 1398 q^{40} - 312 q^{41} + 1964 q^{42} - 3404 q^{43} - 6260 q^{44} - 2532 q^{45} + 466 q^{46} - 838 q^{47} + 3644 q^{48} - 3361 q^{49} - 5648 q^{50} - 256 q^{51} - 24430 q^{52} - 16342 q^{53} - 11472 q^{54} - 4690 q^{55} - 12918 q^{56} - 9228 q^{57} + 5714 q^{58} - 4260 q^{59} - 7620 q^{60} + 6234 q^{61} + 12342 q^{62} - 4566 q^{63} + 15004 q^{64} + 4386 q^{65} + 8594 q^{66} + 8198 q^{67} + 2834 q^{68} + 444 q^{69} - 1456 q^{70} + 16326 q^{71} + 10660 q^{72} + 5410 q^{73} + 7170 q^{74} + 7856 q^{75} + 9676 q^{76} + 6783 q^{77} + 3480 q^{78} + 4186 q^{79} + 26118 q^{80} + 13252 q^{81} - 3232 q^{82} + 19706 q^{83} + 31034 q^{84} + 7766 q^{85} + 24688 q^{86} + 9084 q^{87} - 27408 q^{88} - 13406 q^{89} - 14308 q^{90} - 14805 q^{91} - 40556 q^{92} - 17868 q^{93} - 15378 q^{94} - 31758 q^{95} - 62140 q^{96} - 9914 q^{97} - 23996 q^{98} - 34926 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(693))\)

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
693.4.a \(\chi_{693}(1, \cdot)\) 693.4.a.a 1 1
693.4.a.b 1
693.4.a.c 1
693.4.a.d 1
693.4.a.e 1
693.4.a.f 1
693.4.a.g 2
693.4.a.h 2
693.4.a.i 2
693.4.a.j 2
693.4.a.k 2
693.4.a.l 4
693.4.a.m 4
693.4.a.n 5
693.4.a.o 5
693.4.a.p 5
693.4.a.q 5
693.4.a.r 8
693.4.a.s 8
693.4.a.t 8
693.4.a.u 8
693.4.c \(\chi_{693}(307, \cdot)\) n/a 118 1
693.4.e \(\chi_{693}(188, \cdot)\) 693.4.e.a 80 1
693.4.g \(\chi_{693}(197, \cdot)\) 693.4.g.a 72 1
693.4.i \(\chi_{693}(100, \cdot)\) n/a 200 2
693.4.j \(\chi_{693}(232, \cdot)\) n/a 360 2
693.4.k \(\chi_{693}(67, \cdot)\) n/a 480 2
693.4.l \(\chi_{693}(529, \cdot)\) n/a 480 2
693.4.m \(\chi_{693}(64, \cdot)\) n/a 360 4
693.4.n \(\chi_{693}(320, \cdot)\) n/a 480 2
693.4.p \(\chi_{693}(241, \cdot)\) n/a 568 2
693.4.r \(\chi_{693}(32, \cdot)\) n/a 568 2
693.4.w \(\chi_{693}(428, \cdot)\) n/a 432 2
693.4.x \(\chi_{693}(296, \cdot)\) n/a 192 2
693.4.ba \(\chi_{693}(439, \cdot)\) n/a 568 2
693.4.bd \(\chi_{693}(419, \cdot)\) n/a 480 2
693.4.be \(\chi_{693}(89, \cdot)\) n/a 160 2
693.4.bg \(\chi_{693}(10, \cdot)\) n/a 236 2
693.4.bj \(\chi_{693}(76, \cdot)\) n/a 568 2
693.4.bk \(\chi_{693}(122, \cdot)\) n/a 480 2
693.4.bn \(\chi_{693}(263, \cdot)\) n/a 568 2
693.4.bq \(\chi_{693}(8, \cdot)\) n/a 288 4
693.4.bs \(\chi_{693}(125, \cdot)\) n/a 384 4
693.4.bu \(\chi_{693}(118, \cdot)\) n/a 472 4
693.4.bw \(\chi_{693}(25, \cdot)\) n/a 2272 8
693.4.bx \(\chi_{693}(4, \cdot)\) n/a 2272 8
693.4.by \(\chi_{693}(37, \cdot)\) n/a 944 8
693.4.bz \(\chi_{693}(148, \cdot)\) n/a 1728 8
693.4.cb \(\chi_{693}(74, \cdot)\) n/a 2272 8
693.4.ce \(\chi_{693}(47, \cdot)\) n/a 2272 8
693.4.cg \(\chi_{693}(19, \cdot)\) n/a 944 8
693.4.ch \(\chi_{693}(13, \cdot)\) n/a 2272 8
693.4.cj \(\chi_{693}(20, \cdot)\) n/a 2272 8
693.4.cm \(\chi_{693}(26, \cdot)\) n/a 768 8
693.4.co \(\chi_{693}(61, \cdot)\) n/a 2272 8
693.4.cq \(\chi_{693}(29, \cdot)\) n/a 1728 8
693.4.ct \(\chi_{693}(107, \cdot)\) n/a 768 8
693.4.cx \(\chi_{693}(2, \cdot)\) n/a 2272 8
693.4.cz \(\chi_{693}(40, \cdot)\) n/a 2272 8
693.4.db \(\chi_{693}(5, \cdot)\) n/a 2272 8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(693))\) into lower level spaces

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