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Properties

Label 4851.2
Level 4851
Weight 2
Dimension 628596
Nonzero newspaces 80
Sturm bound 3386880

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Defining parameters

Level: \( N \) = \( 4851 = 3^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(3386880\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4851))\).

Total New Old
Modular forms 856320 636452 219868
Cusp forms 837121 628596 208525
Eisenstein series 19199 7856 11343

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4851))\)

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
4851.2.a \(\chi_{4851}(1, \cdot)\) 4851.2.a.a 1 1
4851.2.a.b 1
4851.2.a.c 1
4851.2.a.d 1
4851.2.a.e 1
4851.2.a.f 1
4851.2.a.g 1
4851.2.a.h 1
4851.2.a.i 1
4851.2.a.j 1
4851.2.a.k 1
4851.2.a.l 1
4851.2.a.m 1
4851.2.a.n 1
4851.2.a.o 1
4851.2.a.p 1
4851.2.a.q 1
4851.2.a.r 1
4851.2.a.s 1
4851.2.a.t 1
4851.2.a.u 2
4851.2.a.v 2
4851.2.a.w 2
4851.2.a.x 2
4851.2.a.y 2
4851.2.a.z 2
4851.2.a.ba 2
4851.2.a.bb 2
4851.2.a.bc 2
4851.2.a.bd 2
4851.2.a.be 2
4851.2.a.bf 2
4851.2.a.bg 2
4851.2.a.bh 2
4851.2.a.bi 3
4851.2.a.bj 3
4851.2.a.bk 3
4851.2.a.bl 3
4851.2.a.bm 3
4851.2.a.bn 3
4851.2.a.bo 3
4851.2.a.bp 3
4851.2.a.bq 4
4851.2.a.br 4
4851.2.a.bs 4
4851.2.a.bt 4
4851.2.a.bu 4
4851.2.a.bv 4
4851.2.a.bw 4
4851.2.a.bx 4
4851.2.a.by 4
4851.2.a.bz 5
4851.2.a.ca 5
4851.2.a.cb 6
4851.2.a.cc 6
4851.2.a.cd 6
4851.2.a.ce 6
4851.2.a.cf 10
4851.2.a.cg 10
4851.2.a.ch 10
4851.2.c \(\chi_{4851}(3772, \cdot)\) n/a 196 1
4851.2.e \(\chi_{4851}(881, \cdot)\) n/a 136 1
4851.2.g \(\chi_{4851}(197, \cdot)\) n/a 164 1
4851.2.i \(\chi_{4851}(1684, \cdot)\) n/a 332 2
4851.2.j \(\chi_{4851}(1618, \cdot)\) n/a 820 2
4851.2.k \(\chi_{4851}(67, \cdot)\) n/a 800 2
4851.2.l \(\chi_{4851}(1255, \cdot)\) n/a 800 2
4851.2.m \(\chi_{4851}(883, \cdot)\) n/a 800 4
4851.2.n \(\chi_{4851}(2432, \cdot)\) n/a 800 2
4851.2.p \(\chi_{4851}(3706, \cdot)\) n/a 944 2
4851.2.r \(\chi_{4851}(1451, \cdot)\) n/a 944 2
4851.2.w \(\chi_{4851}(1814, \cdot)\) n/a 964 2
4851.2.x \(\chi_{4851}(1880, \cdot)\) n/a 320 2
4851.2.ba \(\chi_{4851}(472, \cdot)\) n/a 944 2
4851.2.bd \(\chi_{4851}(2498, \cdot)\) n/a 800 2
4851.2.be \(\chi_{4851}(2861, \cdot)\) n/a 264 2
4851.2.bg \(\chi_{4851}(901, \cdot)\) n/a 392 2
4851.2.bj \(\chi_{4851}(538, \cdot)\) n/a 944 2
4851.2.bk \(\chi_{4851}(815, \cdot)\) n/a 800 2
4851.2.bn \(\chi_{4851}(263, \cdot)\) n/a 944 2
4851.2.bp \(\chi_{4851}(694, \cdot)\) n/a 1392 6
4851.2.br \(\chi_{4851}(1520, \cdot)\) n/a 656 4
4851.2.bt \(\chi_{4851}(1763, \cdot)\) n/a 640 4
4851.2.bv \(\chi_{4851}(244, \cdot)\) n/a 784 4
4851.2.by \(\chi_{4851}(890, \cdot)\) n/a 1344 6
4851.2.ca \(\chi_{4851}(188, \cdot)\) n/a 1104 6
4851.2.cc \(\chi_{4851}(307, \cdot)\) n/a 1668 6
4851.2.ce \(\chi_{4851}(214, \cdot)\) n/a 3776 8
4851.2.cf \(\chi_{4851}(520, \cdot)\) n/a 3776 8
4851.2.cg \(\chi_{4851}(361, \cdot)\) n/a 1568 8
4851.2.ch \(\chi_{4851}(148, \cdot)\) n/a 3856 8
4851.2.ci \(\chi_{4851}(529, \cdot)\) n/a 6720 12
4851.2.cj \(\chi_{4851}(331, \cdot)\) n/a 6720 12
4851.2.ck \(\chi_{4851}(232, \cdot)\) n/a 6720 12
4851.2.cl \(\chi_{4851}(100, \cdot)\) n/a 2808 12
4851.2.cn \(\chi_{4851}(1157, \cdot)\) n/a 3776 8
4851.2.cq \(\chi_{4851}(1697, \cdot)\) n/a 3776 8
4851.2.cs \(\chi_{4851}(19, \cdot)\) n/a 1568 8
4851.2.ct \(\chi_{4851}(391, \cdot)\) n/a 3776 8
4851.2.cv \(\chi_{4851}(146, \cdot)\) n/a 3776 8
4851.2.cy \(\chi_{4851}(80, \cdot)\) n/a 1280 8
4851.2.da \(\chi_{4851}(754, \cdot)\) n/a 3776 8
4851.2.dc \(\chi_{4851}(50, \cdot)\) n/a 3856 8
4851.2.df \(\chi_{4851}(116, \cdot)\) n/a 1280 8
4851.2.dj \(\chi_{4851}(128, \cdot)\) n/a 3776 8
4851.2.dl \(\chi_{4851}(178, \cdot)\) n/a 3776 8
4851.2.dn \(\chi_{4851}(509, \cdot)\) n/a 3776 8
4851.2.do \(\chi_{4851}(64, \cdot)\) n/a 6672 24
4851.2.dq \(\chi_{4851}(527, \cdot)\) n/a 8016 12
4851.2.dt \(\chi_{4851}(122, \cdot)\) n/a 6720 12
4851.2.du \(\chi_{4851}(76, \cdot)\) n/a 8016 12
4851.2.dx \(\chi_{4851}(10, \cdot)\) n/a 3336 12
4851.2.dz \(\chi_{4851}(89, \cdot)\) n/a 2256 12
4851.2.ea \(\chi_{4851}(419, \cdot)\) n/a 6720 12
4851.2.ed \(\chi_{4851}(439, \cdot)\) n/a 8016 12
4851.2.eg \(\chi_{4851}(296, \cdot)\) n/a 2688 12
4851.2.eh \(\chi_{4851}(428, \cdot)\) n/a 8016 12
4851.2.em \(\chi_{4851}(32, \cdot)\) n/a 8016 12
4851.2.eo \(\chi_{4851}(241, \cdot)\) n/a 8016 12
4851.2.eq \(\chi_{4851}(320, \cdot)\) n/a 6720 12
4851.2.es \(\chi_{4851}(118, \cdot)\) n/a 6672 24
4851.2.eu \(\chi_{4851}(125, \cdot)\) n/a 5376 24
4851.2.ew \(\chi_{4851}(8, \cdot)\) n/a 5376 24
4851.2.ey \(\chi_{4851}(169, \cdot)\) n/a 32064 48
4851.2.ez \(\chi_{4851}(37, \cdot)\) n/a 13344 48
4851.2.fa \(\chi_{4851}(4, \cdot)\) n/a 32064 48
4851.2.fb \(\chi_{4851}(25, \cdot)\) n/a 32064 48
4851.2.fc \(\chi_{4851}(5, \cdot)\) n/a 32064 48
4851.2.fe \(\chi_{4851}(40, \cdot)\) n/a 32064 48
4851.2.fg \(\chi_{4851}(2, \cdot)\) n/a 32064 48
4851.2.fk \(\chi_{4851}(107, \cdot)\) n/a 10752 48
4851.2.fn \(\chi_{4851}(29, \cdot)\) n/a 32064 48
4851.2.fp \(\chi_{4851}(61, \cdot)\) n/a 32064 48
4851.2.fr \(\chi_{4851}(26, \cdot)\) n/a 10752 48
4851.2.fu \(\chi_{4851}(20, \cdot)\) n/a 32064 48
4851.2.fw \(\chi_{4851}(13, \cdot)\) n/a 32064 48
4851.2.fx \(\chi_{4851}(73, \cdot)\) n/a 13344 48
4851.2.fz \(\chi_{4851}(47, \cdot)\) n/a 32064 48
4851.2.gc \(\chi_{4851}(74, \cdot)\) n/a 32064 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4851))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4851)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(693))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1617))\)\(^{\oplus 2}\)