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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

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

Display 100 coefficients 10 coefficients

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

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