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Properties

Label 6468.2
Level 6468
Weight 2
Dimension 464326
Nonzero newspaces 64
Sturm bound 4515840

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Defining parameters

Level: \( N \) = \( 6468 = 2^{2} \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(4515840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6468))\).

Total New Old
Modular forms 1140960 467814 673146
Cusp forms 1116961 464326 652635
Eisenstein series 23999 3488 20511

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6468))\)

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
6468.2.a \(\chi_{6468}(1, \cdot)\) 6468.2.a.a 1 1
6468.2.a.b 1
6468.2.a.c 1
6468.2.a.d 1
6468.2.a.e 1
6468.2.a.f 1
6468.2.a.g 1
6468.2.a.h 1
6468.2.a.i 1
6468.2.a.j 1
6468.2.a.k 1
6468.2.a.l 1
6468.2.a.m 1
6468.2.a.n 1
6468.2.a.o 1
6468.2.a.p 1
6468.2.a.q 1
6468.2.a.r 1
6468.2.a.s 1
6468.2.a.t 1
6468.2.a.u 2
6468.2.a.v 2
6468.2.a.w 2
6468.2.a.x 2
6468.2.a.y 4
6468.2.a.z 4
6468.2.a.ba 5
6468.2.a.bb 5
6468.2.a.bc 6
6468.2.a.bd 6
6468.2.a.be 6
6468.2.a.bf 6
6468.2.c \(\chi_{6468}(6271, \cdot)\) n/a 400 1
6468.2.d \(\chi_{6468}(197, \cdot)\) n/a 164 1
6468.2.f \(\chi_{6468}(1079, \cdot)\) n/a 820 1
6468.2.i \(\chi_{6468}(5389, \cdot)\) 6468.2.i.a 32 1
6468.2.i.b 48
6468.2.k \(\chi_{6468}(5587, \cdot)\) n/a 492 1
6468.2.l \(\chi_{6468}(881, \cdot)\) n/a 132 1
6468.2.n \(\chi_{6468}(6467, \cdot)\) n/a 944 1
6468.2.q \(\chi_{6468}(3301, \cdot)\) n/a 132 2
6468.2.r \(\chi_{6468}(1765, \cdot)\) n/a 328 4
6468.2.t \(\chi_{6468}(2861, \cdot)\) n/a 268 2
6468.2.u \(\chi_{6468}(2419, \cdot)\) n/a 960 2
6468.2.y \(\chi_{6468}(1979, \cdot)\) n/a 1888 2
6468.2.ba \(\chi_{6468}(3497, \cdot)\) n/a 320 2
6468.2.bb \(\chi_{6468}(1783, \cdot)\) n/a 800 2
6468.2.bd \(\chi_{6468}(901, \cdot)\) n/a 160 2
6468.2.bg \(\chi_{6468}(4379, \cdot)\) n/a 1600 2
6468.2.bh \(\chi_{6468}(925, \cdot)\) n/a 552 6
6468.2.bk \(\chi_{6468}(2351, \cdot)\) n/a 3776 4
6468.2.bm \(\chi_{6468}(2645, \cdot)\) n/a 640 4
6468.2.bn \(\chi_{6468}(1471, \cdot)\) n/a 1968 4
6468.2.bp \(\chi_{6468}(1273, \cdot)\) n/a 320 4
6468.2.bs \(\chi_{6468}(2843, \cdot)\) n/a 3856 4
6468.2.bu \(\chi_{6468}(2549, \cdot)\) n/a 656 4
6468.2.bv \(\chi_{6468}(1567, \cdot)\) n/a 1920 4
6468.2.by \(\chi_{6468}(923, \cdot)\) n/a 8016 6
6468.2.ca \(\chi_{6468}(1805, \cdot)\) n/a 1128 6
6468.2.cd \(\chi_{6468}(43, \cdot)\) n/a 4032 6
6468.2.cf \(\chi_{6468}(769, \cdot)\) n/a 672 6
6468.2.cg \(\chi_{6468}(155, \cdot)\) n/a 6720 6
6468.2.ci \(\chi_{6468}(1121, \cdot)\) n/a 1344 6
6468.2.cl \(\chi_{6468}(727, \cdot)\) n/a 3360 6
6468.2.cm \(\chi_{6468}(361, \cdot)\) n/a 640 8
6468.2.cn \(\chi_{6468}(529, \cdot)\) n/a 1128 12
6468.2.co \(\chi_{6468}(851, \cdot)\) n/a 7552 8
6468.2.cr \(\chi_{6468}(325, \cdot)\) n/a 640 8
6468.2.ct \(\chi_{6468}(31, \cdot)\) n/a 3840 8
6468.2.cu \(\chi_{6468}(557, \cdot)\) n/a 1280 8
6468.2.cw \(\chi_{6468}(215, \cdot)\) n/a 7552 8
6468.2.da \(\chi_{6468}(79, \cdot)\) n/a 3840 8
6468.2.db \(\chi_{6468}(509, \cdot)\) n/a 1280 8
6468.2.dd \(\chi_{6468}(169, \cdot)\) n/a 2688 24
6468.2.df \(\chi_{6468}(23, \cdot)\) n/a 13440 12
6468.2.dg \(\chi_{6468}(241, \cdot)\) n/a 1344 12
6468.2.di \(\chi_{6468}(199, \cdot)\) n/a 6720 12
6468.2.dl \(\chi_{6468}(65, \cdot)\) n/a 2688 12
6468.2.dn \(\chi_{6468}(131, \cdot)\) n/a 16032 12
6468.2.dp \(\chi_{6468}(571, \cdot)\) n/a 8064 12
6468.2.ds \(\chi_{6468}(89, \cdot)\) n/a 2232 12
6468.2.dt \(\chi_{6468}(223, \cdot)\) n/a 16128 24
6468.2.dw \(\chi_{6468}(29, \cdot)\) n/a 5376 24
6468.2.dy \(\chi_{6468}(71, \cdot)\) n/a 32064 24
6468.2.dz \(\chi_{6468}(13, \cdot)\) n/a 2688 24
6468.2.eb \(\chi_{6468}(127, \cdot)\) n/a 16128 24
6468.2.ee \(\chi_{6468}(125, \cdot)\) n/a 5376 24
6468.2.eg \(\chi_{6468}(83, \cdot)\) n/a 32064 24
6468.2.ei \(\chi_{6468}(25, \cdot)\) n/a 5376 48
6468.2.ej \(\chi_{6468}(5, \cdot)\) n/a 10752 48
6468.2.em \(\chi_{6468}(151, \cdot)\) n/a 32256 48
6468.2.eo \(\chi_{6468}(299, \cdot)\) n/a 64128 48
6468.2.eq \(\chi_{6468}(149, \cdot)\) n/a 10752 48
6468.2.et \(\chi_{6468}(103, \cdot)\) n/a 32256 48
6468.2.ev \(\chi_{6468}(61, \cdot)\) n/a 5376 48
6468.2.ew \(\chi_{6468}(179, \cdot)\) n/a 64128 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6468))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6468)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(924))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1078))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1617))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3234))\)\(^{\oplus 2}\)