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Properties

Label 6664.2
Level 6664
Weight 2
Dimension 723280
Nonzero newspaces 60
Sturm bound 5419008

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Defining parameters

Level: \( N \) = \( 6664 = 2^{3} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(5419008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6664))\).

Total New Old
Modular forms 1366272 729100 637172
Cusp forms 1343233 723280 619953
Eisenstein series 23039 5820 17219

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6664))\)

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
6664.2.a \(\chi_{6664}(1, \cdot)\) 6664.2.a.a 1 1
6664.2.a.b 1
6664.2.a.c 1
6664.2.a.d 1
6664.2.a.e 1
6664.2.a.f 1
6664.2.a.g 2
6664.2.a.h 2
6664.2.a.i 2
6664.2.a.j 3
6664.2.a.k 3
6664.2.a.l 3
6664.2.a.m 3
6664.2.a.n 4
6664.2.a.o 4
6664.2.a.p 6
6664.2.a.q 6
6664.2.a.r 6
6664.2.a.s 6
6664.2.a.t 6
6664.2.a.u 6
6664.2.a.v 7
6664.2.a.w 7
6664.2.a.x 7
6664.2.a.y 7
6664.2.a.z 10
6664.2.a.ba 10
6664.2.a.bb 12
6664.2.a.bc 12
6664.2.a.bd 12
6664.2.a.be 12
6664.2.b \(\chi_{6664}(3333, \cdot)\) n/a 656 1
6664.2.c \(\chi_{6664}(5881, \cdot)\) n/a 184 1
6664.2.h \(\chi_{6664}(6663, \cdot)\) None 0 1
6664.2.i \(\chi_{6664}(4115, \cdot)\) n/a 640 1
6664.2.j \(\chi_{6664}(783, \cdot)\) None 0 1
6664.2.k \(\chi_{6664}(3331, \cdot)\) n/a 712 1
6664.2.p \(\chi_{6664}(2549, \cdot)\) n/a 728 1
6664.2.q \(\chi_{6664}(4489, \cdot)\) n/a 320 2
6664.2.s \(\chi_{6664}(1373, \cdot)\) n/a 1456 2
6664.2.t \(\chi_{6664}(1959, \cdot)\) None 0 2
6664.2.w \(\chi_{6664}(1177, \cdot)\) n/a 368 2
6664.2.x \(\chi_{6664}(2155, \cdot)\) n/a 1424 2
6664.2.z \(\chi_{6664}(373, \cdot)\) n/a 1424 2
6664.2.be \(\chi_{6664}(1599, \cdot)\) None 0 2
6664.2.bf \(\chi_{6664}(4147, \cdot)\) n/a 1424 2
6664.2.bg \(\chi_{6664}(815, \cdot)\) None 0 2
6664.2.bh \(\chi_{6664}(4931, \cdot)\) n/a 1280 2
6664.2.bm \(\chi_{6664}(1157, \cdot)\) n/a 1280 2
6664.2.bn \(\chi_{6664}(3705, \cdot)\) n/a 360 2
6664.2.bo \(\chi_{6664}(953, \cdot)\) n/a 1344 6
6664.2.bp \(\chi_{6664}(195, \cdot)\) n/a 2848 4
6664.2.br \(\chi_{6664}(393, \cdot)\) n/a 740 4
6664.2.bt \(\chi_{6664}(1175, \cdot)\) None 0 4
6664.2.bv \(\chi_{6664}(2157, \cdot)\) n/a 2912 4
6664.2.bx \(\chi_{6664}(557, \cdot)\) n/a 2848 4
6664.2.ca \(\chi_{6664}(999, \cdot)\) None 0 4
6664.2.cb \(\chi_{6664}(361, \cdot)\) n/a 720 4
6664.2.ce \(\chi_{6664}(803, \cdot)\) n/a 2848 4
6664.2.cf \(\chi_{6664}(645, \cdot)\) n/a 6024 6
6664.2.ck \(\chi_{6664}(475, \cdot)\) n/a 6024 6
6664.2.cl \(\chi_{6664}(1735, \cdot)\) None 0 6
6664.2.cm \(\chi_{6664}(307, \cdot)\) n/a 5376 6
6664.2.cn \(\chi_{6664}(951, \cdot)\) None 0 6
6664.2.cs \(\chi_{6664}(169, \cdot)\) n/a 1512 6
6664.2.ct \(\chi_{6664}(477, \cdot)\) n/a 5376 6
6664.2.cu \(\chi_{6664}(99, \cdot)\) n/a 5824 8
6664.2.cx \(\chi_{6664}(295, \cdot)\) None 0 8
6664.2.cy \(\chi_{6664}(97, \cdot)\) n/a 1440 8
6664.2.db \(\chi_{6664}(685, \cdot)\) n/a 5696 8
6664.2.dc \(\chi_{6664}(137, \cdot)\) n/a 2688 12
6664.2.de \(\chi_{6664}(569, \cdot)\) n/a 1440 8
6664.2.dg \(\chi_{6664}(19, \cdot)\) n/a 5696 8
6664.2.di \(\chi_{6664}(1341, \cdot)\) n/a 5696 8
6664.2.dk \(\chi_{6664}(423, \cdot)\) None 0 8
6664.2.dm \(\chi_{6664}(251, \cdot)\) n/a 12048 12
6664.2.dn \(\chi_{6664}(225, \cdot)\) n/a 3024 12
6664.2.dq \(\chi_{6664}(55, \cdot)\) None 0 12
6664.2.dr \(\chi_{6664}(421, \cdot)\) n/a 12048 12
6664.2.dt \(\chi_{6664}(305, \cdot)\) n/a 3024 12
6664.2.du \(\chi_{6664}(205, \cdot)\) n/a 10752 12
6664.2.dz \(\chi_{6664}(171, \cdot)\) n/a 10752 12
6664.2.ea \(\chi_{6664}(271, \cdot)\) None 0 12
6664.2.eb \(\chi_{6664}(339, \cdot)\) n/a 12048 12
6664.2.ec \(\chi_{6664}(103, \cdot)\) None 0 12
6664.2.eh \(\chi_{6664}(781, \cdot)\) n/a 12048 12
6664.2.ej \(\chi_{6664}(717, \cdot)\) n/a 11392 16
6664.2.ek \(\chi_{6664}(129, \cdot)\) n/a 2880 16
6664.2.en \(\chi_{6664}(79, \cdot)\) None 0 16
6664.2.eo \(\chi_{6664}(275, \cdot)\) n/a 11392 16
6664.2.er \(\chi_{6664}(253, \cdot)\) n/a 24096 24
6664.2.et \(\chi_{6664}(111, \cdot)\) None 0 24
6664.2.ev \(\chi_{6664}(281, \cdot)\) n/a 6048 24
6664.2.ex \(\chi_{6664}(83, \cdot)\) n/a 24096 24
6664.2.ey \(\chi_{6664}(115, \cdot)\) n/a 24096 24
6664.2.fb \(\chi_{6664}(81, \cdot)\) n/a 6048 24
6664.2.fc \(\chi_{6664}(47, \cdot)\) None 0 24
6664.2.ff \(\chi_{6664}(149, \cdot)\) n/a 24096 24
6664.2.fh \(\chi_{6664}(41, \cdot)\) n/a 12096 48
6664.2.fi \(\chi_{6664}(125, \cdot)\) n/a 48192 48
6664.2.fl \(\chi_{6664}(211, \cdot)\) n/a 48192 48
6664.2.fm \(\chi_{6664}(71, \cdot)\) None 0 48
6664.2.fo \(\chi_{6664}(87, \cdot)\) None 0 48
6664.2.fq \(\chi_{6664}(53, \cdot)\) n/a 48192 48
6664.2.fs \(\chi_{6664}(59, \cdot)\) n/a 48192 48
6664.2.fu \(\chi_{6664}(9, \cdot)\) n/a 12096 48
6664.2.fw \(\chi_{6664}(23, \cdot)\) None 0 96
6664.2.fz \(\chi_{6664}(11, \cdot)\) n/a 96384 96
6664.2.ga \(\chi_{6664}(5, \cdot)\) n/a 96384 96
6664.2.gd \(\chi_{6664}(73, \cdot)\) n/a 24192 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6664))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6664)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(833))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(952))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1666))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3332))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6664))\)\(^{\oplus 1}\)