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Properties

Label 8820.2
Level 8820
Weight 2
Dimension 822877
Nonzero newspaces 120
Sturm bound 8128512

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Defining parameters

Level: \( N \) = \( 8820 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(8128512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8820))\).

Total New Old
Modular forms 2051328 828117 1223211
Cusp forms 2012929 822877 1190052
Eisenstein series 38399 5240 33159

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8820))\)

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
8820.2.a \(\chi_{8820}(1, \cdot)\) 8820.2.a.a 1 1
8820.2.a.b 1
8820.2.a.c 1
8820.2.a.d 1
8820.2.a.e 1
8820.2.a.f 1
8820.2.a.g 1
8820.2.a.h 1
8820.2.a.i 1
8820.2.a.j 1
8820.2.a.k 1
8820.2.a.l 1
8820.2.a.m 1
8820.2.a.n 1
8820.2.a.o 1
8820.2.a.p 1
8820.2.a.q 1
8820.2.a.r 1
8820.2.a.s 1
8820.2.a.t 1
8820.2.a.u 1
8820.2.a.v 1
8820.2.a.w 1
8820.2.a.x 1
8820.2.a.y 1
8820.2.a.z 1
8820.2.a.ba 1
8820.2.a.bb 1
8820.2.a.bc 1
8820.2.a.bd 2
8820.2.a.be 2
8820.2.a.bf 2
8820.2.a.bg 2
8820.2.a.bh 2
8820.2.a.bi 2
8820.2.a.bj 2
8820.2.a.bk 2
8820.2.a.bl 2
8820.2.a.bm 2
8820.2.a.bn 3
8820.2.a.bo 3
8820.2.a.bp 3
8820.2.a.bq 3
8820.2.a.br 4
8820.2.a.bs 4
8820.2.c \(\chi_{8820}(3331, \cdot)\) n/a 400 1
8820.2.d \(\chi_{8820}(881, \cdot)\) 8820.2.d.a 12 1
8820.2.d.b 12
8820.2.d.c 16
8820.2.d.d 16
8820.2.f \(\chi_{8820}(4409, \cdot)\) 8820.2.f.a 32 1
8820.2.f.b 48
8820.2.i \(\chi_{8820}(6859, \cdot)\) n/a 592 1
8820.2.k \(\chi_{8820}(3529, \cdot)\) n/a 102 1
8820.2.l \(\chi_{8820}(1079, \cdot)\) n/a 492 1
8820.2.n \(\chi_{8820}(6371, \cdot)\) n/a 328 1
8820.2.q \(\chi_{8820}(3301, \cdot)\) n/a 320 2
8820.2.r \(\chi_{8820}(2941, \cdot)\) n/a 328 2
8820.2.s \(\chi_{8820}(361, \cdot)\) n/a 132 2
8820.2.t \(\chi_{8820}(961, \cdot)\) n/a 320 2
8820.2.v \(\chi_{8820}(197, \cdot)\) n/a 164 2
8820.2.w \(\chi_{8820}(883, \cdot)\) n/a 1210 2
8820.2.z \(\chi_{8820}(1763, \cdot)\) n/a 960 2
8820.2.ba \(\chi_{8820}(4213, \cdot)\) n/a 200 2
8820.2.bc \(\chi_{8820}(2959, \cdot)\) n/a 2848 2
8820.2.bf \(\chi_{8820}(3449, \cdot)\) n/a 480 2
8820.2.bh \(\chi_{8820}(3461, \cdot)\) n/a 320 2
8820.2.bi \(\chi_{8820}(31, \cdot)\) n/a 1920 2
8820.2.bl \(\chi_{8820}(1439, \cdot)\) n/a 960 2
8820.2.bm \(\chi_{8820}(1549, \cdot)\) n/a 200 2
8820.2.bo \(\chi_{8820}(491, \cdot)\) n/a 1968 2
8820.2.bs \(\chi_{8820}(3791, \cdot)\) n/a 1920 2
8820.2.bv \(\chi_{8820}(589, \cdot)\) n/a 492 2
8820.2.bx \(\chi_{8820}(2039, \cdot)\) n/a 2848 2
8820.2.by \(\chi_{8820}(6829, \cdot)\) n/a 480 2
8820.2.ca \(\chi_{8820}(4019, \cdot)\) n/a 2912 2
8820.2.ce \(\chi_{8820}(4391, \cdot)\) n/a 640 2
8820.2.cg \(\chi_{8820}(521, \cdot)\) n/a 104 2
8820.2.ch \(\chi_{8820}(2971, \cdot)\) n/a 800 2
8820.2.cj \(\chi_{8820}(1469, \cdot)\) n/a 480 2
8820.2.cl \(\chi_{8820}(619, \cdot)\) n/a 2848 2
8820.2.co \(\chi_{8820}(509, \cdot)\) n/a 480 2
8820.2.cq \(\chi_{8820}(979, \cdot)\) n/a 2848 2
8820.2.cs \(\chi_{8820}(391, \cdot)\) n/a 1920 2
8820.2.cu \(\chi_{8820}(5801, \cdot)\) n/a 320 2
8820.2.cv \(\chi_{8820}(2371, \cdot)\) n/a 1920 2
8820.2.cx \(\chi_{8820}(3821, \cdot)\) n/a 320 2
8820.2.cz \(\chi_{8820}(19, \cdot)\) n/a 1184 2
8820.2.dc \(\chi_{8820}(4049, \cdot)\) n/a 160 2
8820.2.df \(\chi_{8820}(851, \cdot)\) n/a 1920 2
8820.2.dh \(\chi_{8820}(4379, \cdot)\) n/a 2848 2
8820.2.di \(\chi_{8820}(949, \cdot)\) n/a 480 2
8820.2.dk \(\chi_{8820}(1261, \cdot)\) n/a 552 6
8820.2.dm \(\chi_{8820}(67, \cdot)\) n/a 5696 4
8820.2.dn \(\chi_{8820}(1733, \cdot)\) n/a 960 4
8820.2.dp \(\chi_{8820}(587, \cdot)\) n/a 5696 4
8820.2.dr \(\chi_{8820}(3853, \cdot)\) n/a 400 4
8820.2.dt \(\chi_{8820}(3253, \cdot)\) n/a 960 4
8820.2.dw \(\chi_{8820}(227, \cdot)\) n/a 5696 4
8820.2.dy \(\chi_{8820}(1403, \cdot)\) n/a 1920 4
8820.2.ea \(\chi_{8820}(97, \cdot)\) n/a 960 4
8820.2.eb \(\chi_{8820}(1373, \cdot)\) n/a 984 4
8820.2.ed \(\chi_{8820}(667, \cdot)\) n/a 2368 4
8820.2.ef \(\chi_{8820}(4183, \cdot)\) n/a 5696 4
8820.2.ei \(\chi_{8820}(1157, \cdot)\) n/a 960 4
8820.2.ek \(\chi_{8820}(557, \cdot)\) n/a 320 4
8820.2.em \(\chi_{8820}(3823, \cdot)\) n/a 5824 4
8820.2.eo \(\chi_{8820}(313, \cdot)\) n/a 960 4
8820.2.ep \(\chi_{8820}(803, \cdot)\) n/a 5696 4
8820.2.es \(\chi_{8820}(71, \cdot)\) n/a 2688 6
8820.2.eu \(\chi_{8820}(2339, \cdot)\) n/a 4032 6
8820.2.ex \(\chi_{8820}(1009, \cdot)\) n/a 840 6
8820.2.ez \(\chi_{8820}(559, \cdot)\) n/a 5016 6
8820.2.fa \(\chi_{8820}(629, \cdot)\) n/a 672 6
8820.2.fc \(\chi_{8820}(2141, \cdot)\) n/a 432 6
8820.2.ff \(\chi_{8820}(811, \cdot)\) n/a 3360 6
8820.2.fg \(\chi_{8820}(1201, \cdot)\) n/a 2688 12
8820.2.fh \(\chi_{8820}(541, \cdot)\) n/a 1128 12
8820.2.fi \(\chi_{8820}(421, \cdot)\) n/a 2688 12
8820.2.fj \(\chi_{8820}(121, \cdot)\) n/a 2688 12
8820.2.fk \(\chi_{8820}(503, \cdot)\) n/a 8064 12
8820.2.fn \(\chi_{8820}(433, \cdot)\) n/a 1680 12
8820.2.fo \(\chi_{8820}(953, \cdot)\) n/a 1344 12
8820.2.fr \(\chi_{8820}(127, \cdot)\) n/a 10032 12
8820.2.fs \(\chi_{8820}(709, \cdot)\) n/a 4032 12
8820.2.fv \(\chi_{8820}(599, \cdot)\) n/a 24096 12
8820.2.fx \(\chi_{8820}(191, \cdot)\) n/a 16128 12
8820.2.ga \(\chi_{8820}(89, \cdot)\) n/a 1344 12
8820.2.gb \(\chi_{8820}(199, \cdot)\) n/a 10032 12
8820.2.gd \(\chi_{8820}(41, \cdot)\) n/a 2688 12
8820.2.gf \(\chi_{8820}(871, \cdot)\) n/a 16128 12
8820.2.gi \(\chi_{8820}(101, \cdot)\) n/a 2688 12
8820.2.gk \(\chi_{8820}(1231, \cdot)\) n/a 16128 12
8820.2.gm \(\chi_{8820}(139, \cdot)\) n/a 24096 12
8820.2.go \(\chi_{8820}(1769, \cdot)\) n/a 4032 12
8820.2.gp \(\chi_{8820}(859, \cdot)\) n/a 24096 12
8820.2.gr \(\chi_{8820}(209, \cdot)\) n/a 4032 12
8820.2.gt \(\chi_{8820}(271, \cdot)\) n/a 6720 12
8820.2.gw \(\chi_{8820}(341, \cdot)\) n/a 912 12
8820.2.gy \(\chi_{8820}(431, \cdot)\) n/a 5376 12
8820.2.ha \(\chi_{8820}(239, \cdot)\) n/a 24096 12
8820.2.hc \(\chi_{8820}(529, \cdot)\) n/a 4032 12
8820.2.hf \(\chi_{8820}(779, \cdot)\) n/a 24096 12
8820.2.hh \(\chi_{8820}(169, \cdot)\) n/a 4032 12
8820.2.hk \(\chi_{8820}(11, \cdot)\) n/a 16128 12
8820.2.hm \(\chi_{8820}(911, \cdot)\) n/a 16128 12
8820.2.ho \(\chi_{8820}(109, \cdot)\) n/a 1680 12
8820.2.hr \(\chi_{8820}(179, \cdot)\) n/a 8064 12
8820.2.hs \(\chi_{8820}(691, \cdot)\) n/a 16128 12
8820.2.hv \(\chi_{8820}(941, \cdot)\) n/a 2688 12
8820.2.hx \(\chi_{8820}(689, \cdot)\) n/a 4032 12
8820.2.hy \(\chi_{8820}(439, \cdot)\) n/a 24096 12
8820.2.ia \(\chi_{8820}(157, \cdot)\) n/a 8064 24
8820.2.id \(\chi_{8820}(47, \cdot)\) n/a 48192 24
8820.2.if \(\chi_{8820}(113, \cdot)\) n/a 8064 24
8820.2.ih \(\chi_{8820}(247, \cdot)\) n/a 48192 24
8820.2.ij \(\chi_{8820}(163, \cdot)\) n/a 20064 24
8820.2.ik \(\chi_{8820}(53, \cdot)\) n/a 2688 24
8820.2.im \(\chi_{8820}(137, \cdot)\) n/a 8064 24
8820.2.io \(\chi_{8820}(43, \cdot)\) n/a 48192 24
8820.2.ir \(\chi_{8820}(83, \cdot)\) n/a 48192 24
8820.2.it \(\chi_{8820}(493, \cdot)\) n/a 8064 24
8820.2.iv \(\chi_{8820}(73, \cdot)\) n/a 3360 24
8820.2.iw \(\chi_{8820}(143, \cdot)\) n/a 16128 24
8820.2.iy \(\chi_{8820}(383, \cdot)\) n/a 48192 24
8820.2.ja \(\chi_{8820}(13, \cdot)\) n/a 8064 24
8820.2.jc \(\chi_{8820}(583, \cdot)\) n/a 48192 24
8820.2.jf \(\chi_{8820}(317, \cdot)\) n/a 8064 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8820))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8820)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 54}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(882))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(980))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1260))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1470))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1764))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2205))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2940))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4410))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8820))\)\(^{\oplus 1}\)