Properties

Label 1716.2
Level 1716
Weight 2
Dimension 33880
Nonzero newspaces 48
Sturm bound 322560
Trace bound 17

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Defining parameters

Level: \( N \) = \( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(322560\)
Trace bound: \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1716))\).

Total New Old
Modular forms 83040 34680 48360
Cusp forms 78241 33880 44361
Eisenstein series 4799 800 3999

Trace form

\( 33880 q - 76 q^{4} - 38 q^{6} - 28 q^{7} - 100 q^{9} + O(q^{10}) \) \( 33880 q - 76 q^{4} - 38 q^{6} - 28 q^{7} - 100 q^{9} - 56 q^{10} - 32 q^{11} - 76 q^{12} - 230 q^{13} + 20 q^{14} - 24 q^{15} + 4 q^{16} + 8 q^{17} + 18 q^{18} + 76 q^{19} + 196 q^{20} + 28 q^{21} + 92 q^{22} + 88 q^{23} + 118 q^{24} + 36 q^{25} + 170 q^{26} + 102 q^{27} + 144 q^{28} + 100 q^{29} + 68 q^{30} + 88 q^{31} + 120 q^{32} + 34 q^{33} - 160 q^{34} + 88 q^{35} - 82 q^{36} + 20 q^{37} - 100 q^{38} + 91 q^{39} - 408 q^{40} + 252 q^{41} - 204 q^{42} + 64 q^{43} - 200 q^{44} + 70 q^{45} - 416 q^{46} + 28 q^{47} - 244 q^{48} + 172 q^{49} - 356 q^{50} + 38 q^{51} - 352 q^{52} + 196 q^{53} - 164 q^{54} - 28 q^{55} - 296 q^{56} - 74 q^{57} - 288 q^{58} - 84 q^{59} - 408 q^{60} - 120 q^{61} - 120 q^{62} - 254 q^{63} - 196 q^{64} - 24 q^{65} - 312 q^{66} - 180 q^{67} - 322 q^{69} - 336 q^{70} - 128 q^{71} - 364 q^{72} - 332 q^{73} - 100 q^{74} - 358 q^{75} - 216 q^{76} - 172 q^{77} - 436 q^{78} - 204 q^{79} - 220 q^{80} - 300 q^{81} - 276 q^{82} - 132 q^{83} - 440 q^{84} - 408 q^{85} - 256 q^{86} - 168 q^{87} - 468 q^{88} - 224 q^{89} - 308 q^{90} - 54 q^{91} - 204 q^{92} - 208 q^{93} - 368 q^{94} - 36 q^{95} - 220 q^{96} - 200 q^{97} - 216 q^{98} + 198 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1716))\)

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
1716.2.a \(\chi_{1716}(1, \cdot)\) 1716.2.a.a 1 1
1716.2.a.b 1
1716.2.a.c 1
1716.2.a.d 2
1716.2.a.e 2
1716.2.a.f 3
1716.2.a.g 3
1716.2.a.h 3
1716.2.a.i 4
1716.2.b \(\chi_{1716}(571, \cdot)\) n/a 168 1
1716.2.c \(\chi_{1716}(287, \cdot)\) n/a 240 1
1716.2.d \(\chi_{1716}(989, \cdot)\) 1716.2.d.a 48 1
1716.2.e \(\chi_{1716}(1585, \cdot)\) 1716.2.e.a 10 1
1716.2.e.b 10
1716.2.n \(\chi_{1716}(703, \cdot)\) n/a 144 1
1716.2.o \(\chi_{1716}(155, \cdot)\) n/a 280 1
1716.2.p \(\chi_{1716}(857, \cdot)\) 1716.2.p.a 56 1
1716.2.q \(\chi_{1716}(133, \cdot)\) 1716.2.q.a 2 2
1716.2.q.b 12
1716.2.q.c 12
1716.2.q.d 12
1716.2.q.e 14
1716.2.r \(\chi_{1716}(395, \cdot)\) n/a 656 2
1716.2.t \(\chi_{1716}(463, \cdot)\) n/a 280 2
1716.2.v \(\chi_{1716}(109, \cdot)\) 1716.2.v.a 4 2
1716.2.v.b 4
1716.2.v.c 20
1716.2.v.d 28
1716.2.x \(\chi_{1716}(749, \cdot)\) 1716.2.x.a 96 2
1716.2.z \(\chi_{1716}(157, \cdot)\) 1716.2.z.a 4 4
1716.2.z.b 4
1716.2.z.c 4
1716.2.z.d 16
1716.2.z.e 20
1716.2.z.f 20
1716.2.z.g 28
1716.2.be \(\chi_{1716}(1057, \cdot)\) 1716.2.be.a 20 2
1716.2.be.b 24
1716.2.bf \(\chi_{1716}(1121, \cdot)\) n/a 112 2
1716.2.bg \(\chi_{1716}(419, \cdot)\) n/a 560 2
1716.2.bh \(\chi_{1716}(43, \cdot)\) n/a 336 2
1716.2.bi \(\chi_{1716}(329, \cdot)\) n/a 112 2
1716.2.bj \(\chi_{1716}(23, \cdot)\) n/a 560 2
1716.2.bk \(\chi_{1716}(835, \cdot)\) n/a 336 2
1716.2.bp \(\chi_{1716}(233, \cdot)\) n/a 224 4
1716.2.bq \(\chi_{1716}(79, \cdot)\) n/a 576 4
1716.2.br \(\chi_{1716}(311, \cdot)\) n/a 1312 4
1716.2.ca \(\chi_{1716}(365, \cdot)\) n/a 192 4
1716.2.cb \(\chi_{1716}(25, \cdot)\) n/a 112 4
1716.2.cc \(\chi_{1716}(259, \cdot)\) n/a 672 4
1716.2.cd \(\chi_{1716}(443, \cdot)\) n/a 1152 4
1716.2.cf \(\chi_{1716}(89, \cdot)\) n/a 184 4
1716.2.ch \(\chi_{1716}(241, \cdot)\) n/a 112 4
1716.2.cj \(\chi_{1716}(67, \cdot)\) n/a 560 4
1716.2.cl \(\chi_{1716}(527, \cdot)\) n/a 1312 4
1716.2.cm \(\chi_{1716}(289, \cdot)\) n/a 224 8
1716.2.co \(\chi_{1716}(73, \cdot)\) n/a 224 8
1716.2.cq \(\chi_{1716}(5, \cdot)\) n/a 448 8
1716.2.cs \(\chi_{1716}(83, \cdot)\) n/a 2624 8
1716.2.cu \(\chi_{1716}(31, \cdot)\) n/a 1344 8
1716.2.cz \(\chi_{1716}(179, \cdot)\) n/a 2624 8
1716.2.da \(\chi_{1716}(139, \cdot)\) n/a 1344 8
1716.2.db \(\chi_{1716}(17, \cdot)\) n/a 448 8
1716.2.dc \(\chi_{1716}(191, \cdot)\) n/a 2624 8
1716.2.dd \(\chi_{1716}(127, \cdot)\) n/a 1344 8
1716.2.de \(\chi_{1716}(49, \cdot)\) n/a 224 8
1716.2.df \(\chi_{1716}(29, \cdot)\) n/a 448 8
1716.2.dk \(\chi_{1716}(115, \cdot)\) n/a 2688 16
1716.2.dm \(\chi_{1716}(167, \cdot)\) n/a 5248 16
1716.2.do \(\chi_{1716}(137, \cdot)\) n/a 896 16
1716.2.dq \(\chi_{1716}(85, \cdot)\) n/a 448 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1716))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1716)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(572))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(858))\)\(^{\oplus 2}\)