Properties

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

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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

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