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Properties

Label 6020.2
Level 6020
Weight 2
Dimension 542416
Nonzero newspaces 120
Sturm bound 4257792

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Defining parameters

Level: \( N \) = \( 6020 = 2^{2} \cdot 5 \cdot 7 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(4257792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6020))\).

Total New Old
Modular forms 1074528 547344 527184
Cusp forms 1054369 542416 511953
Eisenstein series 20159 4928 15231

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6020))\)

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
6020.2.a \(\chi_{6020}(1, \cdot)\) 6020.2.a.a 1 1
6020.2.a.b 1
6020.2.a.c 1
6020.2.a.d 7
6020.2.a.e 7
6020.2.a.f 8
6020.2.a.g 9
6020.2.a.h 12
6020.2.a.i 12
6020.2.a.j 13
6020.2.a.k 13
6020.2.c \(\chi_{6020}(4299, \cdot)\) n/a 792 1
6020.2.e \(\chi_{6020}(1119, \cdot)\) n/a 1008 1
6020.2.g \(\chi_{6020}(2409, \cdot)\) n/a 124 1
6020.2.i \(\chi_{6020}(3009, \cdot)\) n/a 176 1
6020.2.k \(\chi_{6020}(4731, \cdot)\) n/a 672 1
6020.2.m \(\chi_{6020}(1891, \cdot)\) n/a 528 1
6020.2.o \(\chi_{6020}(601, \cdot)\) n/a 120 1
6020.2.q \(\chi_{6020}(221, \cdot)\) n/a 236 2
6020.2.r \(\chi_{6020}(3441, \cdot)\) n/a 224 2
6020.2.s \(\chi_{6020}(1541, \cdot)\) n/a 176 2
6020.2.t \(\chi_{6020}(1941, \cdot)\) n/a 236 2
6020.2.w \(\chi_{6020}(603, \cdot)\) n/a 1512 2
6020.2.x \(\chi_{6020}(1203, \cdot)\) n/a 2096 2
6020.2.ba \(\chi_{6020}(517, \cdot)\) n/a 336 2
6020.2.bb \(\chi_{6020}(2493, \cdot)\) n/a 264 2
6020.2.bc \(\chi_{6020}(1069, \cdot)\) n/a 352 2
6020.2.be \(\chi_{6020}(1369, \cdot)\) n/a 352 2
6020.2.bg \(\chi_{6020}(4779, \cdot)\) n/a 2096 2
6020.2.bi \(\chi_{6020}(179, \cdot)\) n/a 2096 2
6020.2.bk \(\chi_{6020}(351, \cdot)\) n/a 1056 2
6020.2.bm \(\chi_{6020}(251, \cdot)\) n/a 1408 2
6020.2.bo \(\chi_{6020}(1461, \cdot)\) n/a 232 2
6020.2.bs \(\chi_{6020}(381, \cdot)\) n/a 236 2
6020.2.bu \(\chi_{6020}(1291, \cdot)\) n/a 1344 2
6020.2.bx \(\chi_{6020}(2531, \cdot)\) n/a 1408 2
6020.2.bz \(\chi_{6020}(1111, \cdot)\) n/a 1408 2
6020.2.ca \(\chi_{6020}(1031, \cdot)\) n/a 1408 2
6020.2.cd \(\chi_{6020}(3821, \cdot)\) n/a 232 2
6020.2.cf \(\chi_{6020}(2659, \cdot)\) n/a 2096 2
6020.2.ch \(\chi_{6020}(1499, \cdot)\) n/a 1584 2
6020.2.cj \(\chi_{6020}(1549, \cdot)\) n/a 336 2
6020.2.cm \(\chi_{6020}(2329, \cdot)\) n/a 352 2
6020.2.co \(\chi_{6020}(2629, \cdot)\) n/a 352 2
6020.2.cp \(\chi_{6020}(3869, \cdot)\) n/a 352 2
6020.2.cr \(\chi_{6020}(1719, \cdot)\) n/a 2096 2
6020.2.cu \(\chi_{6020}(479, \cdot)\) n/a 2096 2
6020.2.cw \(\chi_{6020}(1899, \cdot)\) n/a 2096 2
6020.2.cx \(\chi_{6020}(1979, \cdot)\) n/a 2016 2
6020.2.cz \(\chi_{6020}(209, \cdot)\) n/a 352 2
6020.2.db \(\chi_{6020}(3949, \cdot)\) n/a 264 2
6020.2.de \(\chi_{6020}(1641, \cdot)\) n/a 236 2
6020.2.dg \(\chi_{6020}(3791, \cdot)\) n/a 1408 2
6020.2.di \(\chi_{6020}(2371, \cdot)\) n/a 1408 2
6020.2.dk \(\chi_{6020}(981, \cdot)\) n/a 528 6
6020.2.dl \(\chi_{6020}(37, \cdot)\) n/a 704 4
6020.2.dm \(\chi_{6020}(2973, \cdot)\) n/a 704 4
6020.2.dp \(\chi_{6020}(467, \cdot)\) n/a 4192 4
6020.2.dq \(\chi_{6020}(767, \cdot)\) n/a 4192 4
6020.2.dt \(\chi_{6020}(867, \cdot)\) n/a 4192 4
6020.2.du \(\chi_{6020}(2143, \cdot)\) n/a 3168 4
6020.2.dz \(\chi_{6020}(173, \cdot)\) n/a 672 4
6020.2.ea \(\chi_{6020}(1117, \cdot)\) n/a 704 4
6020.2.ed \(\chi_{6020}(93, \cdot)\) n/a 704 4
6020.2.ee \(\chi_{6020}(1713, \cdot)\) n/a 704 4
6020.2.eh \(\chi_{6020}(947, \cdot)\) n/a 4032 4
6020.2.ei \(\chi_{6020}(2063, \cdot)\) n/a 4192 4
6020.2.el \(\chi_{6020}(523, \cdot)\) n/a 4192 4
6020.2.em \(\chi_{6020}(823, \cdot)\) n/a 4192 4
6020.2.en \(\chi_{6020}(897, \cdot)\) n/a 528 4
6020.2.eo \(\chi_{6020}(853, \cdot)\) n/a 704 4
6020.2.es \(\chi_{6020}(1021, \cdot)\) n/a 720 6
6020.2.eu \(\chi_{6020}(211, \cdot)\) n/a 3168 6
6020.2.ew \(\chi_{6020}(391, \cdot)\) n/a 4224 6
6020.2.ey \(\chi_{6020}(629, \cdot)\) n/a 1056 6
6020.2.fa \(\chi_{6020}(729, \cdot)\) n/a 792 6
6020.2.fc \(\chi_{6020}(279, \cdot)\) n/a 6288 6
6020.2.fe \(\chi_{6020}(1919, \cdot)\) n/a 4752 6
6020.2.fg \(\chi_{6020}(361, \cdot)\) n/a 1416 12
6020.2.fh \(\chi_{6020}(281, \cdot)\) n/a 1056 12
6020.2.fi \(\chi_{6020}(121, \cdot)\) n/a 1392 12
6020.2.fj \(\chi_{6020}(81, \cdot)\) n/a 1416 12
6020.2.fk \(\chi_{6020}(113, \cdot)\) n/a 1584 12
6020.2.fl \(\chi_{6020}(97, \cdot)\) n/a 2112 12
6020.2.fo \(\chi_{6020}(27, \cdot)\) n/a 12576 12
6020.2.fp \(\chi_{6020}(127, \cdot)\) n/a 9504 12
6020.2.ft \(\chi_{6020}(411, \cdot)\) n/a 8448 12
6020.2.fv \(\chi_{6020}(191, \cdot)\) n/a 8448 12
6020.2.fx \(\chi_{6020}(241, \cdot)\) n/a 1416 12
6020.2.ga \(\chi_{6020}(169, \cdot)\) n/a 1584 12
6020.2.gc \(\chi_{6020}(69, \cdot)\) n/a 2112 12
6020.2.ge \(\chi_{6020}(59, \cdot)\) n/a 12576 12
6020.2.gf \(\chi_{6020}(499, \cdot)\) n/a 12576 12
6020.2.gh \(\chi_{6020}(339, \cdot)\) n/a 12576 12
6020.2.gk \(\chi_{6020}(39, \cdot)\) n/a 12576 12
6020.2.gm \(\chi_{6020}(409, \cdot)\) n/a 2112 12
6020.2.gn \(\chi_{6020}(9, \cdot)\) n/a 2112 12
6020.2.gp \(\chi_{6020}(549, \cdot)\) n/a 2112 12
6020.2.gs \(\chi_{6020}(709, \cdot)\) n/a 2112 12
6020.2.gu \(\chi_{6020}(519, \cdot)\) n/a 9504 12
6020.2.gw \(\chi_{6020}(139, \cdot)\) n/a 12576 12
6020.2.gy \(\chi_{6020}(321, \cdot)\) n/a 1392 12
6020.2.hb \(\chi_{6020}(51, \cdot)\) n/a 8448 12
6020.2.hc \(\chi_{6020}(31, \cdot)\) n/a 8448 12
6020.2.he \(\chi_{6020}(291, \cdot)\) n/a 8448 12
6020.2.hh \(\chi_{6020}(451, \cdot)\) n/a 8448 12
6020.2.hj \(\chi_{6020}(61, \cdot)\) n/a 1416 12
6020.2.hn \(\chi_{6020}(481, \cdot)\) n/a 1392 12
6020.2.hp \(\chi_{6020}(111, \cdot)\) n/a 8448 12
6020.2.hr \(\chi_{6020}(71, \cdot)\) n/a 6336 12
6020.2.ht \(\chi_{6020}(319, \cdot)\) n/a 12576 12
6020.2.hv \(\chi_{6020}(619, \cdot)\) n/a 12576 12
6020.2.hx \(\chi_{6020}(289, \cdot)\) n/a 2112 12
6020.2.hz \(\chi_{6020}(89, \cdot)\) n/a 2112 12
6020.2.ic \(\chi_{6020}(13, \cdot)\) n/a 4224 24
6020.2.id \(\chi_{6020}(673, \cdot)\) n/a 3168 24
6020.2.ie \(\chi_{6020}(67, \cdot)\) n/a 25152 24
6020.2.if \(\chi_{6020}(3, \cdot)\) n/a 25152 24
6020.2.ii \(\chi_{6020}(383, \cdot)\) n/a 25152 24
6020.2.ij \(\chi_{6020}(107, \cdot)\) n/a 25152 24
6020.2.im \(\chi_{6020}(633, \cdot)\) n/a 4224 24
6020.2.in \(\chi_{6020}(233, \cdot)\) n/a 4224 24
6020.2.iq \(\chi_{6020}(137, \cdot)\) n/a 4224 24
6020.2.ir \(\chi_{6020}(213, \cdot)\) n/a 4224 24
6020.2.iw \(\chi_{6020}(267, \cdot)\) n/a 19008 24
6020.2.ix \(\chi_{6020}(363, \cdot)\) n/a 25152 24
6020.2.ja \(\chi_{6020}(23, \cdot)\) n/a 25152 24
6020.2.jb \(\chi_{6020}(507, \cdot)\) n/a 25152 24
6020.2.je \(\chi_{6020}(17, \cdot)\) n/a 4224 24
6020.2.jf \(\chi_{6020}(177, \cdot)\) n/a 4224 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6020))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6020)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(172))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(215))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(301))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(430))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(602))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(860))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1204))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1505))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3010))\)\(^{\oplus 2}\)