# Properties

 Label 3969.2 Level 3969 Weight 2 Dimension 430628 Nonzero newspaces 44 Sturm bound 2286144 Trace bound 23

## Defining parameters

 Level: $$N$$ = $$3969 = 3^{4} \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$44$$ Sturm bound: $$2286144$$ Trace bound: $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3969))$$.

Total New Old
Modular forms 578016 436060 141956
Cusp forms 565057 430628 134429
Eisenstein series 12959 5432 7527

## Trace form

 $$430628 q - 372 q^{2} - 558 q^{3} - 622 q^{4} - 375 q^{5} - 558 q^{6} - 720 q^{7} - 672 q^{8} - 558 q^{9} + O(q^{10})$$ $$430628 q - 372 q^{2} - 558 q^{3} - 622 q^{4} - 375 q^{5} - 558 q^{6} - 720 q^{7} - 672 q^{8} - 558 q^{9} - 909 q^{10} - 381 q^{11} - 558 q^{12} - 629 q^{13} - 432 q^{14} - 990 q^{15} - 622 q^{16} - 387 q^{17} - 549 q^{18} - 893 q^{19} - 339 q^{20} - 648 q^{21} - 1095 q^{22} - 339 q^{23} - 504 q^{24} - 610 q^{25} - 285 q^{26} - 531 q^{27} - 1044 q^{28} - 633 q^{29} - 504 q^{30} - 611 q^{31} - 324 q^{32} - 531 q^{33} - 609 q^{34} - 432 q^{35} - 954 q^{36} - 911 q^{37} - 411 q^{38} - 558 q^{39} - 549 q^{40} - 375 q^{41} - 648 q^{42} - 1103 q^{43} - 309 q^{44} - 504 q^{45} - 855 q^{46} - 309 q^{47} - 459 q^{48} - 702 q^{49} - 876 q^{50} - 495 q^{51} - 437 q^{52} - 117 q^{53} - 432 q^{54} - 711 q^{55} - 252 q^{56} - 936 q^{57} - 381 q^{58} - 123 q^{59} - 441 q^{60} - 497 q^{61} + 57 q^{62} - 648 q^{63} - 1294 q^{64} - 111 q^{65} - 558 q^{66} - 503 q^{67} - 36 q^{68} - 612 q^{69} - 612 q^{70} - 621 q^{71} - 774 q^{72} - 794 q^{73} - 339 q^{74} - 648 q^{75} - 455 q^{76} - 378 q^{77} - 1107 q^{78} - 587 q^{79} - 402 q^{80} - 630 q^{81} - 1752 q^{82} - 489 q^{83} - 648 q^{84} - 1071 q^{85} - 573 q^{86} - 702 q^{87} - 471 q^{88} - 450 q^{89} - 639 q^{90} - 1044 q^{91} - 753 q^{92} - 540 q^{93} - 579 q^{94} - 309 q^{95} - 567 q^{96} - 569 q^{97} - 432 q^{98} - 1674 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3969))$$

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
3969.2.a $$\chi_{3969}(1, \cdot)$$ 3969.2.a.a 1 1
3969.2.a.b 1
3969.2.a.c 1
3969.2.a.d 1
3969.2.a.e 1
3969.2.a.f 1
3969.2.a.g 2
3969.2.a.h 2
3969.2.a.i 2
3969.2.a.j 2
3969.2.a.k 2
3969.2.a.l 3
3969.2.a.m 3
3969.2.a.n 3
3969.2.a.o 3
3969.2.a.p 3
3969.2.a.q 3
3969.2.a.r 4
3969.2.a.s 4
3969.2.a.t 4
3969.2.a.u 4
3969.2.a.v 4
3969.2.a.w 4
3969.2.a.x 4
3969.2.a.y 4
3969.2.a.z 5
3969.2.a.ba 5
3969.2.a.bb 5
3969.2.a.bc 5
3969.2.a.bd 6
3969.2.a.be 6
3969.2.a.bf 8
3969.2.a.bg 8
3969.2.a.bh 12
3969.2.a.bi 12
3969.2.a.bj 16
3969.2.c $$\chi_{3969}(3968, \cdot)$$ n/a 152 1
3969.2.e $$\chi_{3969}(2431, \cdot)$$ n/a 304 2
3969.2.f $$\chi_{3969}(1324, \cdot)$$ n/a 318 2
3969.2.g $$\chi_{3969}(1108, \cdot)$$ n/a 312 2
3969.2.h $$\chi_{3969}(2566, \cdot)$$ n/a 312 2
3969.2.i $$\chi_{3969}(215, \cdot)$$ n/a 312 2
3969.2.o $$\chi_{3969}(1322, \cdot)$$ n/a 312 2
3969.2.p $$\chi_{3969}(80, \cdot)$$ n/a 304 2
3969.2.s $$\chi_{3969}(2726, \cdot)$$ n/a 312 2
3969.2.u $$\chi_{3969}(568, \cdot)$$ n/a 1320 6
3969.2.v $$\chi_{3969}(361, \cdot)$$ n/a 696 6
3969.2.w $$\chi_{3969}(442, \cdot)$$ n/a 708 6
3969.2.x $$\chi_{3969}(226, \cdot)$$ n/a 696 6
3969.2.z $$\chi_{3969}(566, \cdot)$$ n/a 1320 6
3969.2.be $$\chi_{3969}(521, \cdot)$$ n/a 696 6
3969.2.bh $$\chi_{3969}(656, \cdot)$$ n/a 696 6
3969.2.bi $$\chi_{3969}(440, \cdot)$$ n/a 696 6
3969.2.bk $$\chi_{3969}(298, \cdot)$$ n/a 2664 12
3969.2.bl $$\chi_{3969}(109, \cdot)$$ n/a 2664 12
3969.2.bm $$\chi_{3969}(190, \cdot)$$ n/a 2664 12
3969.2.bn $$\chi_{3969}(163, \cdot)$$ n/a 2640 12
3969.2.bo $$\chi_{3969}(67, \cdot)$$ n/a 6408 18
3969.2.bp $$\chi_{3969}(148, \cdot)$$ n/a 6552 18
3969.2.bq $$\chi_{3969}(214, \cdot)$$ n/a 6408 18
3969.2.bs $$\chi_{3969}(26, \cdot)$$ n/a 2664 12
3969.2.bv $$\chi_{3969}(404, \cdot)$$ n/a 2640 12
3969.2.bw $$\chi_{3969}(188, \cdot)$$ n/a 2664 12
3969.2.cc $$\chi_{3969}(269, \cdot)$$ n/a 2664 12
3969.2.cf $$\chi_{3969}(362, \cdot)$$ n/a 6408 18
3969.2.cg $$\chi_{3969}(146, \cdot)$$ n/a 6408 18
3969.2.cl $$\chi_{3969}(68, \cdot)$$ n/a 6408 18
3969.2.cm $$\chi_{3969}(37, \cdot)$$ n/a 5976 36
3969.2.cn $$\chi_{3969}(64, \cdot)$$ n/a 5976 36
3969.2.co $$\chi_{3969}(100, \cdot)$$ n/a 5976 36
3969.2.cq $$\chi_{3969}(62, \cdot)$$ n/a 5976 36
3969.2.cr $$\chi_{3969}(17, \cdot)$$ n/a 5976 36
3969.2.cu $$\chi_{3969}(143, \cdot)$$ n/a 5976 36
3969.2.cy $$\chi_{3969}(25, \cdot)$$ n/a 54216 108
3969.2.cz $$\chi_{3969}(4, \cdot)$$ n/a 54216 108
3969.2.da $$\chi_{3969}(22, \cdot)$$ n/a 54216 108
3969.2.db $$\chi_{3969}(5, \cdot)$$ n/a 54216 108
3969.2.dg $$\chi_{3969}(47, \cdot)$$ n/a 54216 108
3969.2.dh $$\chi_{3969}(20, \cdot)$$ n/a 54216 108

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3969))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3969)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(189))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(441))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(567))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1323))$$$$^{\oplus 2}$$