Properties

Label 4730.2
Level 4730
Weight 2
Dimension 199669
Nonzero newspaces 48
Sturm bound 2661120

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Defining parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(2661120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4730))\).

Total New Old
Modular forms 672000 199669 472331
Cusp forms 658561 199669 458892
Eisenstein series 13439 0 13439

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4730))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
4730.2.a \(\chi_{4730}(1, \cdot)\) 4730.2.a.a 1 1
4730.2.a.b 1
4730.2.a.c 1
4730.2.a.d 1
4730.2.a.e 1
4730.2.a.f 1
4730.2.a.g 1
4730.2.a.h 1
4730.2.a.i 1
4730.2.a.j 1
4730.2.a.k 1
4730.2.a.l 2
4730.2.a.m 2
4730.2.a.n 2
4730.2.a.o 2
4730.2.a.p 2
4730.2.a.q 2
4730.2.a.r 2
4730.2.a.s 2
4730.2.a.t 3
4730.2.a.u 4
4730.2.a.v 5
4730.2.a.w 8
4730.2.a.x 8
4730.2.a.y 8
4730.2.a.z 10
4730.2.a.ba 10
4730.2.a.bb 11
4730.2.a.bc 11
4730.2.a.bd 11
4730.2.a.be 12
4730.2.a.bf 13
4730.2.b \(\chi_{4730}(2839, \cdot)\) n/a 208 1
4730.2.d \(\chi_{4730}(1891, \cdot)\) n/a 176 1
4730.2.g \(\chi_{4730}(4729, \cdot)\) n/a 264 1
4730.2.i \(\chi_{4730}(221, \cdot)\) n/a 288 2
4730.2.l \(\chi_{4730}(87, \cdot)\) n/a 504 2
4730.2.m \(\chi_{4730}(3697, \cdot)\) n/a 440 2
4730.2.n \(\chi_{4730}(861, \cdot)\) n/a 672 4
4730.2.p \(\chi_{4730}(3189, \cdot)\) n/a 528 2
4730.2.s \(\chi_{4730}(351, \cdot)\) n/a 352 2
4730.2.u \(\chi_{4730}(3059, \cdot)\) n/a 440 2
4730.2.v \(\chi_{4730}(441, \cdot)\) n/a 912 6
4730.2.x \(\chi_{4730}(1289, \cdot)\) n/a 1056 4
4730.2.ba \(\chi_{4730}(171, \cdot)\) n/a 704 4
4730.2.bc \(\chi_{4730}(1549, \cdot)\) n/a 1008 4
4730.2.bd \(\chi_{4730}(307, \cdot)\) n/a 1056 4
4730.2.be \(\chi_{4730}(2157, \cdot)\) n/a 880 4
4730.2.bh \(\chi_{4730}(1759, \cdot)\) n/a 1584 6
4730.2.bl \(\chi_{4730}(1079, \cdot)\) n/a 1320 6
4730.2.bn \(\chi_{4730}(131, \cdot)\) n/a 1056 6
4730.2.bo \(\chi_{4730}(251, \cdot)\) n/a 1408 8
4730.2.bp \(\chi_{4730}(173, \cdot)\) n/a 2016 8
4730.2.bq \(\chi_{4730}(257, \cdot)\) n/a 2112 8
4730.2.bt \(\chi_{4730}(111, \cdot)\) n/a 1728 12
4730.2.bu \(\chi_{4730}(727, \cdot)\) n/a 2640 12
4730.2.bv \(\chi_{4730}(527, \cdot)\) n/a 3168 12
4730.2.by \(\chi_{4730}(49, \cdot)\) n/a 2112 8
4730.2.ca \(\chi_{4730}(381, \cdot)\) n/a 1408 8
4730.2.cd \(\chi_{4730}(1069, \cdot)\) n/a 2112 8
4730.2.cf \(\chi_{4730}(471, \cdot)\) n/a 4224 24
4730.2.cg \(\chi_{4730}(241, \cdot)\) n/a 2112 12
4730.2.ci \(\chi_{4730}(529, \cdot)\) n/a 2640 12
4730.2.cm \(\chi_{4730}(329, \cdot)\) n/a 3168 12
4730.2.cp \(\chi_{4730}(337, \cdot)\) n/a 4224 16
4730.2.cq \(\chi_{4730}(37, \cdot)\) n/a 4224 16
4730.2.cr \(\chi_{4730}(51, \cdot)\) n/a 4224 24
4730.2.ct \(\chi_{4730}(59, \cdot)\) n/a 6336 24
4730.2.cx \(\chi_{4730}(39, \cdot)\) n/a 6336 24
4730.2.da \(\chi_{4730}(177, \cdot)\) n/a 5280 24
4730.2.db \(\chi_{4730}(153, \cdot)\) n/a 6336 24
4730.2.dc \(\chi_{4730}(31, \cdot)\) n/a 8448 48
4730.2.df \(\chi_{4730}(27, \cdot)\) n/a 12672 48
4730.2.dg \(\chi_{4730}(107, \cdot)\) n/a 12672 48
4730.2.dh \(\chi_{4730}(19, \cdot)\) n/a 12672 48
4730.2.dl \(\chi_{4730}(9, \cdot)\) n/a 12672 48
4730.2.dn \(\chi_{4730}(61, \cdot)\) n/a 8448 48
4730.2.do \(\chi_{4730}(3, \cdot)\) n/a 25344 96
4730.2.dp \(\chi_{4730}(13, \cdot)\) n/a 25344 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4730))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4730)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(215))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(430))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(473))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(946))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2365))\)\(^{\oplus 2}\)