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Properties

Label 3564.2
Level 3564
Weight 2
Dimension 157584
Nonzero newspaces 32
Sturm bound 1399680
Trace bound 23

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Defining parameters

Level: \( N \) = \( 3564 = 2^{2} \cdot 3^{4} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(1399680\)
Trace bound: \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3564))\).

Total New Old
Modular forms 355320 159600 195720
Cusp forms 344521 157584 186937
Eisenstein series 10799 2016 8783

Trace form

\( 157584 q - 96 q^{2} - 160 q^{4} - 186 q^{5} - 144 q^{6} + 6 q^{7} - 102 q^{8} - 288 q^{9} + O(q^{10}) \) \( 157584 q - 96 q^{2} - 160 q^{4} - 186 q^{5} - 144 q^{6} + 6 q^{7} - 102 q^{8} - 288 q^{9} - 240 q^{10} + 3 q^{11} - 324 q^{12} - 326 q^{13} - 126 q^{14} - 184 q^{16} - 228 q^{17} - 144 q^{18} - 36 q^{19} - 138 q^{20} - 342 q^{21} - 188 q^{22} - 114 q^{23} - 144 q^{24} - 394 q^{25} - 66 q^{26} - 54 q^{27} - 224 q^{28} - 318 q^{29} - 144 q^{30} - 54 q^{31} - 36 q^{32} - 351 q^{33} - 296 q^{34} - 96 q^{35} - 144 q^{36} - 512 q^{37} - 48 q^{38} - 54 q^{40} - 174 q^{41} - 54 q^{42} + 54 q^{43} + 33 q^{44} - 540 q^{45} - 56 q^{46} + 198 q^{47} + 54 q^{48} - 234 q^{49} + 324 q^{50} + 126 q^{51} - 18 q^{52} + 108 q^{53} + 108 q^{54} + 90 q^{55} + 246 q^{56} - 180 q^{57} - 18 q^{58} + 246 q^{59} + 90 q^{60} - 206 q^{61} + 294 q^{62} + 108 q^{63} - 52 q^{64} + 102 q^{65} - 90 q^{66} + 18 q^{67} + 108 q^{68} - 108 q^{69} - 38 q^{70} + 120 q^{71} - 144 q^{72} - 434 q^{73} - 42 q^{74} + 180 q^{75} - 68 q^{76} - 123 q^{77} - 378 q^{78} - 114 q^{79} - 120 q^{80} - 144 q^{81} - 492 q^{82} - 36 q^{83} - 90 q^{84} - 384 q^{85} - 144 q^{86} + 288 q^{87} - 260 q^{88} - 420 q^{89} - 270 q^{90} - 90 q^{91} - 510 q^{92} + 108 q^{93} - 350 q^{94} + 24 q^{95} - 378 q^{96} - 362 q^{97} - 756 q^{98} + 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3564))\)

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
3564.2.a \(\chi_{3564}(1, \cdot)\) 3564.2.a.a 1 1
3564.2.a.b 1
3564.2.a.c 1
3564.2.a.d 1
3564.2.a.e 1
3564.2.a.f 1
3564.2.a.g 2
3564.2.a.h 2
3564.2.a.i 2
3564.2.a.j 2
3564.2.a.k 3
3564.2.a.l 3
3564.2.a.m 4
3564.2.a.n 4
3564.2.a.o 6
3564.2.a.p 6
3564.2.b \(\chi_{3564}(1781, \cdot)\) 3564.2.b.a 4 1
3564.2.b.b 4
3564.2.b.c 16
3564.2.b.d 24
3564.2.c \(\chi_{3564}(2267, \cdot)\) n/a 240 1
3564.2.h \(\chi_{3564}(3079, \cdot)\) n/a 280 1
3564.2.i \(\chi_{3564}(1189, \cdot)\) 3564.2.i.a 2 2
3564.2.i.b 2
3564.2.i.c 2
3564.2.i.d 2
3564.2.i.e 2
3564.2.i.f 2
3564.2.i.g 2
3564.2.i.h 2
3564.2.i.i 2
3564.2.i.j 2
3564.2.i.k 4
3564.2.i.l 4
3564.2.i.m 4
3564.2.i.n 4
3564.2.i.o 4
3564.2.i.p 4
3564.2.i.q 6
3564.2.i.r 6
3564.2.i.s 12
3564.2.i.t 12
3564.2.j \(\chi_{3564}(973, \cdot)\) n/a 192 4
3564.2.k \(\chi_{3564}(703, \cdot)\) n/a 568 2
3564.2.p \(\chi_{3564}(1079, \cdot)\) n/a 480 2
3564.2.q \(\chi_{3564}(593, \cdot)\) 3564.2.q.a 4 2
3564.2.q.b 4
3564.2.q.c 4
3564.2.q.d 4
3564.2.q.e 8
3564.2.q.f 8
3564.2.q.g 16
3564.2.q.h 48
3564.2.r \(\chi_{3564}(397, \cdot)\) n/a 180 6
3564.2.s \(\chi_{3564}(811, \cdot)\) n/a 1120 4
3564.2.x \(\chi_{3564}(323, \cdot)\) n/a 1120 4
3564.2.y \(\chi_{3564}(161, \cdot)\) n/a 192 4
3564.2.z \(\chi_{3564}(433, \cdot)\) n/a 384 8
3564.2.bb \(\chi_{3564}(197, \cdot)\) n/a 216 6
3564.2.bd \(\chi_{3564}(307, \cdot)\) n/a 1272 6
3564.2.bf \(\chi_{3564}(287, \cdot)\) n/a 1080 6
3564.2.bh \(\chi_{3564}(133, \cdot)\) n/a 1620 18
3564.2.bi \(\chi_{3564}(701, \cdot)\) n/a 384 8
3564.2.bj \(\chi_{3564}(863, \cdot)\) n/a 2272 8
3564.2.bo \(\chi_{3564}(271, \cdot)\) n/a 2272 8
3564.2.bp \(\chi_{3564}(37, \cdot)\) n/a 864 24
3564.2.bq \(\chi_{3564}(43, \cdot)\) n/a 11592 18
3564.2.bt \(\chi_{3564}(23, \cdot)\) n/a 9720 18
3564.2.bu \(\chi_{3564}(65, \cdot)\) n/a 1944 18
3564.2.by \(\chi_{3564}(71, \cdot)\) n/a 5088 24
3564.2.ca \(\chi_{3564}(19, \cdot)\) n/a 5088 24
3564.2.cc \(\chi_{3564}(17, \cdot)\) n/a 864 24
3564.2.ce \(\chi_{3564}(25, \cdot)\) n/a 7776 72
3564.2.ch \(\chi_{3564}(47, \cdot)\) n/a 46368 72
3564.2.ci \(\chi_{3564}(29, \cdot)\) n/a 7776 72
3564.2.cl \(\chi_{3564}(7, \cdot)\) n/a 46368 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3564))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3564)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(594))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(891))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1188))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1782))\)\(^{\oplus 2}\)