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Properties

Label 4900.2
Level 4900
Weight 2
Dimension 362047
Nonzero newspaces 48
Sturm bound 2822400

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Defining parameters

Level: \( N \) = \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(2822400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4900))\).

Total New Old
Modular forms 714000 366023 347977
Cusp forms 697201 362047 335154
Eisenstein series 16799 3976 12823

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4900))\)

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
4900.2.a \(\chi_{4900}(1, \cdot)\) 4900.2.a.a 1 1
4900.2.a.b 1
4900.2.a.c 1
4900.2.a.d 1
4900.2.a.e 1
4900.2.a.f 1
4900.2.a.g 1
4900.2.a.h 1
4900.2.a.i 1
4900.2.a.j 1
4900.2.a.k 1
4900.2.a.l 1
4900.2.a.m 1
4900.2.a.n 1
4900.2.a.o 1
4900.2.a.p 1
4900.2.a.q 1
4900.2.a.r 1
4900.2.a.s 1
4900.2.a.t 1
4900.2.a.u 1
4900.2.a.v 1
4900.2.a.w 1
4900.2.a.x 2
4900.2.a.y 2
4900.2.a.z 2
4900.2.a.ba 3
4900.2.a.bb 3
4900.2.a.bc 3
4900.2.a.bd 3
4900.2.a.be 4
4900.2.a.bf 4
4900.2.a.bg 4
4900.2.a.bh 4
4900.2.a.bi 4
4900.2.a.bj 4
4900.2.c \(\chi_{4900}(4899, \cdot)\) n/a 352 1
4900.2.e \(\chi_{4900}(2549, \cdot)\) 4900.2.e.a 2 1
4900.2.e.b 2
4900.2.e.c 2
4900.2.e.d 2
4900.2.e.e 2
4900.2.e.f 2
4900.2.e.g 2
4900.2.e.h 2
4900.2.e.i 2
4900.2.e.j 2
4900.2.e.k 2
4900.2.e.l 2
4900.2.e.m 2
4900.2.e.n 2
4900.2.e.o 2
4900.2.e.p 4
4900.2.e.q 4
4900.2.e.r 4
4900.2.e.s 6
4900.2.e.t 6
4900.2.e.u 8
4900.2.g \(\chi_{4900}(2351, \cdot)\) n/a 368 1
4900.2.i \(\chi_{4900}(3301, \cdot)\) n/a 126 2
4900.2.k \(\chi_{4900}(2843, \cdot)\) n/a 718 2
4900.2.m \(\chi_{4900}(293, \cdot)\) n/a 120 2
4900.2.n \(\chi_{4900}(981, \cdot)\) n/a 412 4
4900.2.p \(\chi_{4900}(3351, \cdot)\) n/a 736 2
4900.2.r \(\chi_{4900}(949, \cdot)\) n/a 120 2
4900.2.t \(\chi_{4900}(999, \cdot)\) n/a 704 2
4900.2.v \(\chi_{4900}(701, \cdot)\) n/a 528 6
4900.2.x \(\chi_{4900}(391, \cdot)\) n/a 2368 4
4900.2.z \(\chi_{4900}(589, \cdot)\) n/a 408 4
4900.2.bb \(\chi_{4900}(979, \cdot)\) n/a 2368 4
4900.2.bd \(\chi_{4900}(1293, \cdot)\) n/a 240 4
4900.2.bf \(\chi_{4900}(1243, \cdot)\) n/a 1408 4
4900.2.bj \(\chi_{4900}(251, \cdot)\) n/a 3156 6
4900.2.bl \(\chi_{4900}(449, \cdot)\) n/a 504 6
4900.2.bn \(\chi_{4900}(699, \cdot)\) n/a 3000 6
4900.2.bo \(\chi_{4900}(361, \cdot)\) n/a 800 8
4900.2.bp \(\chi_{4900}(97, \cdot)\) n/a 800 8
4900.2.br \(\chi_{4900}(687, \cdot)\) n/a 4840 8
4900.2.bt \(\chi_{4900}(401, \cdot)\) n/a 1068 12
4900.2.bv \(\chi_{4900}(657, \cdot)\) n/a 1008 12
4900.2.bx \(\chi_{4900}(43, \cdot)\) n/a 6000 12
4900.2.bz \(\chi_{4900}(19, \cdot)\) n/a 4736 8
4900.2.cb \(\chi_{4900}(569, \cdot)\) n/a 800 8
4900.2.cd \(\chi_{4900}(31, \cdot)\) n/a 4736 8
4900.2.cf \(\chi_{4900}(141, \cdot)\) n/a 3360 24
4900.2.cg \(\chi_{4900}(199, \cdot)\) n/a 6000 12
4900.2.ci \(\chi_{4900}(149, \cdot)\) n/a 1008 12
4900.2.ck \(\chi_{4900}(451, \cdot)\) n/a 6312 12
4900.2.co \(\chi_{4900}(67, \cdot)\) n/a 9472 16
4900.2.cq \(\chi_{4900}(117, \cdot)\) n/a 1600 16
4900.2.cr \(\chi_{4900}(139, \cdot)\) n/a 20064 24
4900.2.ct \(\chi_{4900}(29, \cdot)\) n/a 3360 24
4900.2.cv \(\chi_{4900}(111, \cdot)\) n/a 20064 24
4900.2.cy \(\chi_{4900}(107, \cdot)\) n/a 12000 24
4900.2.da \(\chi_{4900}(157, \cdot)\) n/a 2016 24
4900.2.dc \(\chi_{4900}(81, \cdot)\) n/a 6720 48
4900.2.dd \(\chi_{4900}(127, \cdot)\) n/a 40128 48
4900.2.df \(\chi_{4900}(13, \cdot)\) n/a 6720 48
4900.2.dj \(\chi_{4900}(131, \cdot)\) n/a 40128 48
4900.2.dl \(\chi_{4900}(9, \cdot)\) n/a 6720 48
4900.2.dn \(\chi_{4900}(59, \cdot)\) n/a 40128 48
4900.2.dp \(\chi_{4900}(17, \cdot)\) n/a 13440 96
4900.2.dr \(\chi_{4900}(23, \cdot)\) n/a 80256 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4900)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(980))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2450))\)\(^{\oplus 2}\)