Properties

Label 4600.2
Level 4600
Weight 2
Dimension 325516
Nonzero newspaces 36
Sturm bound 2534400

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Defining parameters

Level: \( N \) = \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(2534400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4600))\).

Total New Old
Modular forms 640992 328960 312032
Cusp forms 626209 325516 300693
Eisenstein series 14783 3444 11339

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4600))\)

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
4600.2.a \(\chi_{4600}(1, \cdot)\) 4600.2.a.a 1 1
4600.2.a.b 1
4600.2.a.c 1
4600.2.a.d 1
4600.2.a.e 1
4600.2.a.f 1
4600.2.a.g 1
4600.2.a.h 1
4600.2.a.i 1
4600.2.a.j 1
4600.2.a.k 1
4600.2.a.l 1
4600.2.a.m 1
4600.2.a.n 1
4600.2.a.o 1
4600.2.a.p 1
4600.2.a.q 2
4600.2.a.r 2
4600.2.a.s 2
4600.2.a.t 2
4600.2.a.u 2
4600.2.a.v 3
4600.2.a.w 3
4600.2.a.x 3
4600.2.a.y 3
4600.2.a.z 3
4600.2.a.ba 4
4600.2.a.bb 4
4600.2.a.bc 5
4600.2.a.bd 5
4600.2.a.be 5
4600.2.a.bf 5
4600.2.a.bg 5
4600.2.a.bh 7
4600.2.a.bi 7
4600.2.a.bj 8
4600.2.a.bk 8
4600.2.b \(\chi_{4600}(2299, \cdot)\) n/a 428 1
4600.2.e \(\chi_{4600}(4049, \cdot)\) 4600.2.e.a 2 1
4600.2.e.b 2
4600.2.e.c 2
4600.2.e.d 2
4600.2.e.e 2
4600.2.e.f 2
4600.2.e.g 2
4600.2.e.h 2
4600.2.e.i 2
4600.2.e.j 2
4600.2.e.k 2
4600.2.e.l 4
4600.2.e.m 4
4600.2.e.n 4
4600.2.e.o 4
4600.2.e.p 6
4600.2.e.q 6
4600.2.e.r 6
4600.2.e.s 6
4600.2.e.t 8
4600.2.e.u 10
4600.2.e.v 10
4600.2.e.w 10
4600.2.f \(\chi_{4600}(2301, \cdot)\) n/a 418 1
4600.2.i \(\chi_{4600}(551, \cdot)\) None 0 1
4600.2.j \(\chi_{4600}(1749, \cdot)\) n/a 396 1
4600.2.m \(\chi_{4600}(4599, \cdot)\) None 0 1
4600.2.n \(\chi_{4600}(2851, \cdot)\) n/a 450 1
4600.2.q \(\chi_{4600}(1057, \cdot)\) n/a 216 2
4600.2.s \(\chi_{4600}(2807, \cdot)\) None 0 2
4600.2.v \(\chi_{4600}(507, \cdot)\) n/a 792 2
4600.2.x \(\chi_{4600}(3357, \cdot)\) n/a 856 2
4600.2.y \(\chi_{4600}(921, \cdot)\) n/a 664 4
4600.2.z \(\chi_{4600}(919, \cdot)\) None 0 4
4600.2.bc \(\chi_{4600}(829, \cdot)\) n/a 2640 4
4600.2.bf \(\chi_{4600}(91, \cdot)\) n/a 2864 4
4600.2.bg \(\chi_{4600}(369, \cdot)\) n/a 656 4
4600.2.bj \(\chi_{4600}(459, \cdot)\) n/a 2864 4
4600.2.bk \(\chi_{4600}(1471, \cdot)\) None 0 4
4600.2.bn \(\chi_{4600}(461, \cdot)\) n/a 2640 4
4600.2.bo \(\chi_{4600}(601, \cdot)\) n/a 1140 10
4600.2.bp \(\chi_{4600}(413, \cdot)\) n/a 5728 8
4600.2.br \(\chi_{4600}(323, \cdot)\) n/a 5280 8
4600.2.bu \(\chi_{4600}(47, \cdot)\) None 0 8
4600.2.bw \(\chi_{4600}(137, \cdot)\) n/a 1440 8
4600.2.bz \(\chi_{4600}(51, \cdot)\) n/a 4500 10
4600.2.ca \(\chi_{4600}(199, \cdot)\) None 0 10
4600.2.cd \(\chi_{4600}(349, \cdot)\) n/a 4280 10
4600.2.ce \(\chi_{4600}(751, \cdot)\) None 0 10
4600.2.ch \(\chi_{4600}(101, \cdot)\) n/a 4500 10
4600.2.ci \(\chi_{4600}(49, \cdot)\) n/a 1080 10
4600.2.cl \(\chi_{4600}(99, \cdot)\) n/a 4280 10
4600.2.cm \(\chi_{4600}(157, \cdot)\) n/a 8560 20
4600.2.co \(\chi_{4600}(243, \cdot)\) n/a 8560 20
4600.2.cr \(\chi_{4600}(407, \cdot)\) None 0 20
4600.2.ct \(\chi_{4600}(57, \cdot)\) n/a 2160 20
4600.2.cu \(\chi_{4600}(41, \cdot)\) n/a 7200 40
4600.2.cv \(\chi_{4600}(141, \cdot)\) n/a 28640 40
4600.2.cy \(\chi_{4600}(111, \cdot)\) None 0 40
4600.2.cz \(\chi_{4600}(19, \cdot)\) n/a 28640 40
4600.2.dc \(\chi_{4600}(9, \cdot)\) n/a 7200 40
4600.2.dd \(\chi_{4600}(11, \cdot)\) n/a 28640 40
4600.2.dg \(\chi_{4600}(29, \cdot)\) n/a 28640 40
4600.2.dj \(\chi_{4600}(79, \cdot)\) None 0 40
4600.2.dk \(\chi_{4600}(17, \cdot)\) n/a 14400 80
4600.2.dm \(\chi_{4600}(87, \cdot)\) None 0 80
4600.2.dp \(\chi_{4600}(3, \cdot)\) n/a 57280 80
4600.2.dr \(\chi_{4600}(37, \cdot)\) n/a 57280 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(575))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1150))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2300))\)\(^{\oplus 2}\)