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Properties

Label 6790.2
Level 6790
Weight 2
Dimension 396613
Nonzero newspaces 110
Sturm bound 5419008

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Defining parameters

Level: \( N \) = \( 6790 = 2 \cdot 5 \cdot 7 \cdot 97 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 110 \)
Sturm bound: \(5419008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6790))\).

Total New Old
Modular forms 1363968 396613 967355
Cusp forms 1345537 396613 948924
Eisenstein series 18431 0 18431

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6790))\)

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
6790.2.a \(\chi_{6790}(1, \cdot)\) 6790.2.a.a 1 1
6790.2.a.b 1
6790.2.a.c 1
6790.2.a.d 1
6790.2.a.e 1
6790.2.a.f 1
6790.2.a.g 1
6790.2.a.h 2
6790.2.a.i 2
6790.2.a.j 2
6790.2.a.k 2
6790.2.a.l 2
6790.2.a.m 2
6790.2.a.n 2
6790.2.a.o 4
6790.2.a.p 6
6790.2.a.q 8
6790.2.a.r 10
6790.2.a.s 10
6790.2.a.t 10
6790.2.a.u 10
6790.2.a.v 10
6790.2.a.w 11
6790.2.a.x 11
6790.2.a.y 11
6790.2.a.z 14
6790.2.a.ba 14
6790.2.a.bb 14
6790.2.a.bc 14
6790.2.a.bd 15
6790.2.c \(\chi_{6790}(1359, \cdot)\) n/a 288 1
6790.2.d \(\chi_{6790}(3879, \cdot)\) n/a 296 1
6790.2.f \(\chi_{6790}(2521, \cdot)\) n/a 196 1
6790.2.i \(\chi_{6790}(4691, \cdot)\) n/a 392 2
6790.2.j \(\chi_{6790}(1941, \cdot)\) n/a 512 2
6790.2.k \(\chi_{6790}(4911, \cdot)\) n/a 520 2
6790.2.l \(\chi_{6790}(1031, \cdot)\) n/a 520 2
6790.2.m \(\chi_{6790}(701, \cdot)\) n/a 392 2
6790.2.p \(\chi_{6790}(3373, \cdot)\) n/a 784 2
6790.2.q \(\chi_{6790}(657, \cdot)\) n/a 784 2
6790.2.t \(\chi_{6790}(1357, \cdot)\) n/a 784 2
6790.2.u \(\chi_{6790}(1553, \cdot)\) n/a 768 2
6790.2.w \(\chi_{6790}(2059, \cdot)\) n/a 592 2
6790.2.z \(\chi_{6790}(5009, \cdot)\) n/a 784 2
6790.2.ba \(\chi_{6790}(2389, \cdot)\) n/a 784 2
6790.2.bd \(\chi_{6790}(1551, \cdot)\) n/a 528 2
6790.2.bf \(\chi_{6790}(3431, \cdot)\) n/a 392 2
6790.2.bk \(\chi_{6790}(2461, \cdot)\) n/a 520 2
6790.2.bl \(\chi_{6790}(389, \cdot)\) n/a 768 2
6790.2.bn \(\chi_{6790}(4789, \cdot)\) n/a 592 2
6790.2.bq \(\chi_{6790}(449, \cdot)\) n/a 592 2
6790.2.bs \(\chi_{6790}(2909, \cdot)\) n/a 784 2
6790.2.bu \(\chi_{6790}(1129, \cdot)\) n/a 784 2
6790.2.bv \(\chi_{6790}(1199, \cdot)\) n/a 784 2
6790.2.bz \(\chi_{6790}(3651, \cdot)\) n/a 520 2
6790.2.ca \(\chi_{6790}(1973, \cdot)\) n/a 1568 4
6790.2.cc \(\chi_{6790}(421, \cdot)\) n/a 784 4
6790.2.cf \(\chi_{6790}(729, \cdot)\) n/a 1184 4
6790.2.ch \(\chi_{6790}(923, \cdot)\) n/a 1568 4
6790.2.ci \(\chi_{6790}(1061, \cdot)\) n/a 1040 4
6790.2.cl \(\chi_{6790}(1439, \cdot)\) n/a 1568 4
6790.2.co \(\chi_{6790}(1849, \cdot)\) n/a 1184 4
6790.2.cp \(\chi_{6790}(1089, \cdot)\) n/a 1568 4
6790.2.cr \(\chi_{6790}(423, \cdot)\) n/a 1568 4
6790.2.cs \(\chi_{6790}(327, \cdot)\) n/a 1568 4
6790.2.cu \(\chi_{6790}(297, \cdot)\) n/a 1568 4
6790.2.cx \(\chi_{6790}(1083, \cdot)\) n/a 1568 4
6790.2.cz \(\chi_{6790}(1277, \cdot)\) n/a 1568 4
6790.2.da \(\chi_{6790}(103, \cdot)\) n/a 1568 4
6790.2.dc \(\chi_{6790}(2267, \cdot)\) n/a 1568 4
6790.2.de \(\chi_{6790}(2523, \cdot)\) n/a 1536 4
6790.2.dh \(\chi_{6790}(2133, \cdot)\) n/a 1568 4
6790.2.dj \(\chi_{6790}(643, \cdot)\) n/a 1568 4
6790.2.dk \(\chi_{6790}(507, \cdot)\) n/a 1568 4
6790.2.dn \(\chi_{6790}(307, \cdot)\) n/a 1568 4
6790.2.do \(\chi_{6790}(867, \cdot)\) n/a 1568 4
6790.2.dr \(\chi_{6790}(313, \cdot)\) n/a 1568 4
6790.2.dt \(\chi_{6790}(1587, \cdot)\) n/a 1568 4
6790.2.du \(\chi_{6790}(1517, \cdot)\) n/a 1568 4
6790.2.dx \(\chi_{6790}(81, \cdot)\) n/a 1040 4
6790.2.ea \(\chi_{6790}(851, \cdot)\) n/a 1056 4
6790.2.eb \(\chi_{6790}(491, \cdot)\) n/a 784 4
6790.2.ec \(\chi_{6790}(879, \cdot)\) n/a 1568 4
6790.2.ee \(\chi_{6790}(27, \cdot)\) n/a 3136 8
6790.2.ei \(\chi_{6790}(1191, \cdot)\) n/a 1568 8
6790.2.ej \(\chi_{6790}(309, \cdot)\) n/a 2336 8
6790.2.el \(\chi_{6790}(1273, \cdot)\) n/a 3136 8
6790.2.em \(\chi_{6790}(1543, \cdot)\) n/a 3136 8
6790.2.eo \(\chi_{6790}(397, \cdot)\) n/a 3136 8
6790.2.ep \(\chi_{6790}(227, \cdot)\) n/a 3136 8
6790.2.eq \(\chi_{6790}(1063, \cdot)\) n/a 3136 8
6790.2.eu \(\chi_{6790}(849, \cdot)\) n/a 3136 8
6790.2.ex \(\chi_{6790}(121, \cdot)\) n/a 2080 8
6790.2.ez \(\chi_{6790}(1121, \cdot)\) n/a 1568 8
6790.2.fb \(\chi_{6790}(9, \cdot)\) n/a 3136 8
6790.2.fd \(\chi_{6790}(809, \cdot)\) n/a 3136 8
6790.2.fe \(\chi_{6790}(1131, \cdot)\) n/a 2112 8
6790.2.fg \(\chi_{6790}(151, \cdot)\) n/a 2080 8
6790.2.fi \(\chi_{6790}(379, \cdot)\) n/a 2368 8
6790.2.fn \(\chi_{6790}(73, \cdot)\) n/a 3136 8
6790.2.fo \(\chi_{6790}(237, \cdot)\) n/a 3136 8
6790.2.fp \(\chi_{6790}(33, \cdot)\) n/a 3136 8
6790.2.fr \(\chi_{6790}(733, \cdot)\) n/a 3136 8
6790.2.ft \(\chi_{6790}(321, \cdot)\) n/a 4096 16
6790.2.fu \(\chi_{6790}(69, \cdot)\) n/a 6272 16
6790.2.fw \(\chi_{6790}(127, \cdot)\) n/a 4704 16
6790.2.fz \(\chi_{6790}(337, \cdot)\) n/a 4704 16
6790.2.gb \(\chi_{6790}(517, \cdot)\) n/a 6272 16
6790.2.gd \(\chi_{6790}(453, \cdot)\) n/a 6272 16
6790.2.ge \(\chi_{6790}(437, \cdot)\) n/a 6272 16
6790.2.gh \(\chi_{6790}(467, \cdot)\) n/a 6272 16
6790.2.gk \(\chi_{6790}(11, \cdot)\) n/a 4160 16
6790.2.gl \(\chi_{6790}(289, \cdot)\) n/a 6272 16
6790.2.gm \(\chi_{6790}(99, \cdot)\) n/a 4672 16
6790.2.gn \(\chi_{6790}(79, \cdot)\) n/a 6272 16
6790.2.go \(\chi_{6790}(221, \cdot)\) n/a 4224 16
6790.2.gp \(\chi_{6790}(141, \cdot)\) n/a 3136 16
6790.2.gw \(\chi_{6790}(219, \cdot)\) n/a 6272 16
6790.2.gx \(\chi_{6790}(751, \cdot)\) n/a 4160 16
6790.2.gy \(\chi_{6790}(283, \cdot)\) n/a 6272 16
6790.2.hb \(\chi_{6790}(3, \cdot)\) n/a 6272 16
6790.2.hc \(\chi_{6790}(647, \cdot)\) n/a 6272 16
6790.2.he \(\chi_{6790}(293, \cdot)\) n/a 6272 16
6790.2.hh \(\chi_{6790}(59, \cdot)\) n/a 12544 32
6790.2.hi \(\chi_{6790}(381, \cdot)\) n/a 8320 32
6790.2.hk \(\chi_{6790}(123, \cdot)\) n/a 12544 32
6790.2.hl \(\chi_{6790}(57, \cdot)\) n/a 9408 32
6790.2.hm \(\chi_{6790}(457, \cdot)\) n/a 12544 32
6790.2.ht \(\chi_{6790}(67, \cdot)\) n/a 12544 32
6790.2.hu \(\chi_{6790}(253, \cdot)\) n/a 9408 32
6790.2.hv \(\chi_{6790}(37, \cdot)\) n/a 12544 32
6790.2.hz \(\chi_{6790}(41, \cdot)\) n/a 8448 32
6790.2.ia \(\chi_{6790}(19, \cdot)\) n/a 12544 32
6790.2.ib \(\chi_{6790}(131, \cdot)\) n/a 8448 32
6790.2.ic \(\chi_{6790}(209, \cdot)\) n/a 12544 32
6790.2.id \(\chi_{6790}(409, \cdot)\) n/a 12544 32
6790.2.ie \(\chi_{6790}(171, \cdot)\) n/a 8320 32
6790.2.ii \(\chi_{6790}(23, \cdot)\) n/a 12544 32
6790.2.il \(\chi_{6790}(177, \cdot)\) n/a 12544 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6790))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6790)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(97))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(194))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(485))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(679))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(970))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1358))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3395))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6790))\)\(^{\oplus 1}\)