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Properties

Label 3822.2
Level 3822
Weight 2
Dimension 93668
Nonzero newspaces 60
Sturm bound 1580544
Trace bound 25

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Defining parameters

Level: \( N \) = \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1580544\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3822))\).

Total New Old
Modular forms 400896 93668 307228
Cusp forms 389377 93668 295709
Eisenstein series 11519 0 11519

Trace form

\( 93668 q + 2 q^{2} - 6 q^{3} - 14 q^{4} - 36 q^{5} - 22 q^{6} - 32 q^{7} - 4 q^{8} - 34 q^{9} + O(q^{10}) \) \( 93668 q + 2 q^{2} - 6 q^{3} - 14 q^{4} - 36 q^{5} - 22 q^{6} - 32 q^{7} - 4 q^{8} - 34 q^{9} - 66 q^{10} - 96 q^{11} - 10 q^{12} - 66 q^{13} - 12 q^{15} - 6 q^{16} - 42 q^{17} + 44 q^{18} - 80 q^{19} + 6 q^{20} + 20 q^{21} + 24 q^{22} - 24 q^{23} + 26 q^{24} - 64 q^{25} - 10 q^{26} - 42 q^{27} - 24 q^{28} - 66 q^{29} - 12 q^{30} - 120 q^{31} + 2 q^{32} - 60 q^{33} - 60 q^{34} - 96 q^{35} - 6 q^{36} + 70 q^{37} + 64 q^{38} + 100 q^{39} + 132 q^{40} + 222 q^{41} + 108 q^{42} + 72 q^{43} + 96 q^{44} + 186 q^{45} + 360 q^{46} + 264 q^{47} + 22 q^{48} + 576 q^{49} + 200 q^{50} + 396 q^{51} + 52 q^{52} + 228 q^{53} + 38 q^{54} + 720 q^{55} + 144 q^{56} + 32 q^{57} + 390 q^{58} + 168 q^{59} + 120 q^{60} + 278 q^{61} + 64 q^{62} + 60 q^{63} - 20 q^{64} - 186 q^{65} - 24 q^{66} - 64 q^{67} - 18 q^{68} - 96 q^{69} - 192 q^{71} - 70 q^{72} - 44 q^{73} + 142 q^{74} + 218 q^{75} + 304 q^{76} + 216 q^{77} + 194 q^{78} + 688 q^{79} - 42 q^{80} + 14 q^{81} + 846 q^{82} + 816 q^{83} + 116 q^{84} + 1362 q^{85} + 376 q^{86} + 996 q^{87} - 24 q^{88} + 1164 q^{89} + 228 q^{90} + 680 q^{91} + 480 q^{92} + 1040 q^{93} + 1128 q^{94} + 1536 q^{95} + 26 q^{96} + 1716 q^{97} + 240 q^{98} + 396 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3822))\)

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
3822.2.a \(\chi_{3822}(1, \cdot)\) 3822.2.a.a 1 1
3822.2.a.b 1
3822.2.a.c 1
3822.2.a.d 1
3822.2.a.e 1
3822.2.a.f 1
3822.2.a.g 1
3822.2.a.h 1
3822.2.a.i 1
3822.2.a.j 1
3822.2.a.k 1
3822.2.a.l 1
3822.2.a.m 1
3822.2.a.n 1
3822.2.a.o 1
3822.2.a.p 1
3822.2.a.q 1
3822.2.a.r 1
3822.2.a.s 1
3822.2.a.t 1
3822.2.a.u 1
3822.2.a.v 1
3822.2.a.w 1
3822.2.a.x 1
3822.2.a.y 1
3822.2.a.z 1
3822.2.a.ba 1
3822.2.a.bb 1
3822.2.a.bc 1
3822.2.a.bd 1
3822.2.a.be 1
3822.2.a.bf 1
3822.2.a.bg 1
3822.2.a.bh 1
3822.2.a.bi 2
3822.2.a.bj 2
3822.2.a.bk 2
3822.2.a.bl 2
3822.2.a.bm 2
3822.2.a.bn 2
3822.2.a.bo 2
3822.2.a.bp 2
3822.2.a.bq 2
3822.2.a.br 2
3822.2.a.bs 2
3822.2.a.bt 2
3822.2.a.bu 2
3822.2.a.bv 3
3822.2.a.bw 3
3822.2.a.bx 4
3822.2.a.by 4
3822.2.a.bz 4
3822.2.a.ca 4
3822.2.c \(\chi_{3822}(883, \cdot)\) 3822.2.c.a 2 1
3822.2.c.b 2
3822.2.c.c 2
3822.2.c.d 2
3822.2.c.e 2
3822.2.c.f 4
3822.2.c.g 4
3822.2.c.h 4
3822.2.c.i 6
3822.2.c.j 6
3822.2.c.k 6
3822.2.c.l 6
3822.2.c.m 10
3822.2.c.n 10
3822.2.c.o 16
3822.2.c.p 16
3822.2.e \(\chi_{3822}(3821, \cdot)\) n/a 184 1
3822.2.g \(\chi_{3822}(2939, \cdot)\) n/a 160 1
3822.2.i \(\chi_{3822}(79, \cdot)\) n/a 160 2
3822.2.j \(\chi_{3822}(2713, \cdot)\) n/a 188 2
3822.2.k \(\chi_{3822}(373, \cdot)\) n/a 188 2
3822.2.l \(\chi_{3822}(295, \cdot)\) n/a 188 2
3822.2.o \(\chi_{3822}(2449, \cdot)\) n/a 192 2
3822.2.p \(\chi_{3822}(785, \cdot)\) n/a 380 2
3822.2.q \(\chi_{3822}(881, \cdot)\) n/a 376 2
3822.2.s \(\chi_{3822}(589, \cdot)\) n/a 192 2
3822.2.u \(\chi_{3822}(3155, \cdot)\) n/a 372 2
3822.2.z \(\chi_{3822}(521, \cdot)\) n/a 320 2
3822.2.bb \(\chi_{3822}(815, \cdot)\) n/a 372 2
3822.2.bd \(\chi_{3822}(361, \cdot)\) n/a 188 2
3822.2.bg \(\chi_{3822}(1403, \cdot)\) n/a 376 2
3822.2.bi \(\chi_{3822}(803, \cdot)\) n/a 372 2
3822.2.bk \(\chi_{3822}(961, \cdot)\) n/a 184 2
3822.2.bm \(\chi_{3822}(1843, \cdot)\) n/a 188 2
3822.2.bn \(\chi_{3822}(2285, \cdot)\) n/a 372 2
3822.2.bq \(\chi_{3822}(2057, \cdot)\) n/a 376 2
3822.2.bs \(\chi_{3822}(547, \cdot)\) n/a 672 6
3822.2.bv \(\chi_{3822}(197, \cdot)\) n/a 768 4
3822.2.bw \(\chi_{3822}(863, \cdot)\) n/a 752 4
3822.2.bx \(\chi_{3822}(557, \cdot)\) n/a 744 4
3822.2.by \(\chi_{3822}(97, \cdot)\) n/a 368 4
3822.2.bz \(\chi_{3822}(19, \cdot)\) n/a 376 4
3822.2.ca \(\chi_{3822}(31, \cdot)\) n/a 368 4
3822.2.ch \(\chi_{3822}(1501, \cdot)\) n/a 376 4
3822.2.ci \(\chi_{3822}(275, \cdot)\) n/a 744 4
3822.2.ck \(\chi_{3822}(209, \cdot)\) n/a 1344 6
3822.2.cm \(\chi_{3822}(545, \cdot)\) n/a 1584 6
3822.2.co \(\chi_{3822}(337, \cdot)\) n/a 768 6
3822.2.cq \(\chi_{3822}(211, \cdot)\) n/a 1584 12
3822.2.cr \(\chi_{3822}(445, \cdot)\) n/a 1560 12
3822.2.cs \(\chi_{3822}(289, \cdot)\) n/a 1560 12
3822.2.ct \(\chi_{3822}(235, \cdot)\) n/a 1344 12
3822.2.cu \(\chi_{3822}(239, \cdot)\) n/a 3168 12
3822.2.cv \(\chi_{3822}(265, \cdot)\) n/a 1536 12
3822.2.cz \(\chi_{3822}(419, \cdot)\) n/a 3120 12
3822.2.dc \(\chi_{3822}(101, \cdot)\) n/a 3144 12
3822.2.dd \(\chi_{3822}(205, \cdot)\) n/a 1560 12
3822.2.df \(\chi_{3822}(25, \cdot)\) n/a 1584 12
3822.2.dh \(\chi_{3822}(17, \cdot)\) n/a 3144 12
3822.2.dj \(\chi_{3822}(311, \cdot)\) n/a 3120 12
3822.2.dm \(\chi_{3822}(121, \cdot)\) n/a 1560 12
3822.2.do \(\chi_{3822}(269, \cdot)\) n/a 3144 12
3822.2.dq \(\chi_{3822}(131, \cdot)\) n/a 2688 12
3822.2.dv \(\chi_{3822}(185, \cdot)\) n/a 3144 12
3822.2.dx \(\chi_{3822}(43, \cdot)\) n/a 1584 12
3822.2.dz \(\chi_{3822}(251, \cdot)\) n/a 3120 12
3822.2.ea \(\chi_{3822}(137, \cdot)\) n/a 6288 24
3822.2.eb \(\chi_{3822}(145, \cdot)\) n/a 3120 24
3822.2.ei \(\chi_{3822}(73, \cdot)\) n/a 3168 24
3822.2.ej \(\chi_{3822}(115, \cdot)\) n/a 3120 24
3822.2.ek \(\chi_{3822}(223, \cdot)\) n/a 3168 24
3822.2.el \(\chi_{3822}(11, \cdot)\) n/a 6288 24
3822.2.em \(\chi_{3822}(317, \cdot)\) n/a 6240 24
3822.2.en \(\chi_{3822}(71, \cdot)\) n/a 6240 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3822))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3822)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(637))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1274))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1911))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3822))\)\(^{\oplus 1}\)