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Properties

Label 28900.2
Level 28900
Weight 2
Dimension 13316777
Nonzero newspaces 72
Sturm bound 99878400

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Defining parameters

Level: \( N \) = \( 28900 = 2^{2} \cdot 5^{2} \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(99878400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(28900))\).

Total New Old
Modular forms 25025600 13346993 11678607
Cusp forms 24913601 13316777 11596824
Eisenstein series 111999 30216 81783

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(28900))\)

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
28900.2.a \(\chi_{28900}(1, \cdot)\) 28900.2.a.a 1 1
28900.2.a.b 1
28900.2.a.c 1
28900.2.a.d 1
28900.2.a.e 1
28900.2.a.f 1
28900.2.a.g 1
28900.2.a.h 1
28900.2.a.i 1
28900.2.a.j 1
28900.2.a.k 1
28900.2.a.l 1
28900.2.a.m 2
28900.2.a.n 2
28900.2.a.o 2
28900.2.a.p 2
28900.2.a.q 2
28900.2.a.r 2
28900.2.a.s 2
28900.2.a.t 2
28900.2.a.u 3
28900.2.a.v 3
28900.2.a.w 3
28900.2.a.x 3
28900.2.a.y 3
28900.2.a.z 3
28900.2.a.ba 3
28900.2.a.bb 3
28900.2.a.bc 3
28900.2.a.bd 3
28900.2.a.be 3
28900.2.a.bf 3
28900.2.a.bg 3
28900.2.a.bh 4
28900.2.a.bi 4
28900.2.a.bj 4
28900.2.a.bk 4
28900.2.a.bl 5
28900.2.a.bm 5
28900.2.a.bn 6
28900.2.a.bo 6
28900.2.a.bp 6
28900.2.a.bq 6
28900.2.a.br 6
28900.2.a.bs 6
28900.2.a.bt 6
28900.2.a.bu 6
28900.2.a.bv 8
28900.2.a.bw 12
28900.2.a.bx 12
28900.2.a.by 12
28900.2.a.bz 12
28900.2.a.ca 12
28900.2.a.cb 12
28900.2.a.cc 12
28900.2.a.cd 15
28900.2.a.ce 15
28900.2.a.cf 15
28900.2.a.cg 15
28900.2.a.ch 24
28900.2.a.ci 24
28900.2.a.cj 24
28900.2.a.ck 24
28900.2.a.cl 40
28900.2.c \(\chi_{28900}(5201, \cdot)\) n/a 428 1
28900.2.e \(\chi_{28900}(9249, \cdot)\) n/a 406 1
28900.2.g \(\chi_{28900}(14449, \cdot)\) n/a 404 1
28900.2.i \(\chi_{28900}(1407, \cdot)\) n/a 4804 2
28900.2.l \(\chi_{28900}(15607, \cdot)\) n/a 4818 2
28900.2.m \(\chi_{28900}(23949, \cdot)\) n/a 808 2
28900.2.o \(\chi_{28900}(14701, \cdot)\) n/a 856 2
28900.2.r \(\chi_{28900}(20807, \cdot)\) n/a 4804 2
28900.2.s \(\chi_{28900}(6107, \cdot)\) n/a 4804 2
28900.2.u \(\chi_{28900}(5781, \cdot)\) n/a 2708 4
28900.2.v \(\chi_{28900}(1001, \cdot)\) n/a 1708 4
28900.2.x \(\chi_{28900}(15207, \cdot)\) n/a 9608 4
28900.2.ba \(\chi_{28900}(16607, \cdot)\) n/a 9608 4
28900.2.bc \(\chi_{28900}(8849, \cdot)\) n/a 1624 4
28900.2.be \(\chi_{28900}(2889, \cdot)\) n/a 2704 4
28900.2.bg \(\chi_{28900}(3469, \cdot)\) n/a 2712 4
28900.2.bi \(\chi_{28900}(10981, \cdot)\) n/a 2696 4
28900.2.bl \(\chi_{28900}(4493, \cdot)\) n/a 3240 8
28900.2.bn \(\chi_{28900}(5451, \cdot)\) n/a 20184 8
28900.2.bo \(\chi_{28900}(1799, \cdot)\) n/a 19216 8
28900.2.bq \(\chi_{28900}(3393, \cdot)\) n/a 3240 8
28900.2.bs \(\chi_{28900}(1701, \cdot)\) n/a 7744 16
28900.2.bu \(\chi_{28900}(327, \cdot)\) n/a 32176 8
28900.2.bv \(\chi_{28900}(3467, \cdot)\) n/a 32176 8
28900.2.by \(\chi_{28900}(2061, \cdot)\) n/a 5392 8
28900.2.ca \(\chi_{28900}(829, \cdot)\) n/a 5408 8
28900.2.cb \(\chi_{28900}(4047, \cdot)\) n/a 32280 8
28900.2.ce \(\chi_{28900}(1483, \cdot)\) n/a 32176 8
28900.2.cg \(\chi_{28900}(849, \cdot)\) n/a 7360 16
28900.2.ci \(\chi_{28900}(749, \cdot)\) n/a 7360 16
28900.2.ck \(\chi_{28900}(101, \cdot)\) n/a 7744 16
28900.2.cm \(\chi_{28900}(1889, \cdot)\) n/a 10784 16
28900.2.cp \(\chi_{28900}(423, \cdot)\) n/a 64352 16
28900.2.cq \(\chi_{28900}(2467, \cdot)\) n/a 64352 16
28900.2.ct \(\chi_{28900}(5381, \cdot)\) n/a 10816 16
28900.2.cv \(\chi_{28900}(1007, \cdot)\) n/a 88000 32
28900.2.cw \(\chi_{28900}(407, \cdot)\) n/a 88000 32
28900.2.cz \(\chi_{28900}(701, \cdot)\) n/a 15488 32
28900.2.db \(\chi_{28900}(149, \cdot)\) n/a 14720 32
28900.2.dc \(\chi_{28900}(307, \cdot)\) n/a 88000 32
28900.2.df \(\chi_{28900}(1143, \cdot)\) n/a 88000 32
28900.2.dh \(\chi_{28900}(653, \cdot)\) n/a 21600 32
28900.2.dj \(\chi_{28900}(1659, \cdot)\) n/a 128704 32
28900.2.dk \(\chi_{28900}(131, \cdot)\) n/a 128704 32
28900.2.dm \(\chi_{28900}(513, \cdot)\) n/a 21600 32
28900.2.do \(\chi_{28900}(341, \cdot)\) n/a 49024 64
28900.2.dp \(\chi_{28900}(49, \cdot)\) n/a 29312 64
28900.2.dr \(\chi_{28900}(43, \cdot)\) n/a 176000 64
28900.2.du \(\chi_{28900}(807, \cdot)\) n/a 176000 64
28900.2.dw \(\chi_{28900}(501, \cdot)\) n/a 31040 64
28900.2.dy \(\chi_{28900}(441, \cdot)\) n/a 49024 64
28900.2.ea \(\chi_{28900}(69, \cdot)\) n/a 48896 64
28900.2.ec \(\chi_{28900}(169, \cdot)\) n/a 48896 64
28900.2.ef \(\chi_{28900}(193, \cdot)\) n/a 58752 128
28900.2.eh \(\chi_{28900}(99, \cdot)\) n/a 352000 128
28900.2.ei \(\chi_{28900}(351, \cdot)\) n/a 371328 128
28900.2.ek \(\chi_{28900}(57, \cdot)\) n/a 58752 128
28900.2.em \(\chi_{28900}(47, \cdot)\) n/a 587008 128
28900.2.ep \(\chi_{28900}(103, \cdot)\) n/a 587008 128
28900.2.eq \(\chi_{28900}(89, \cdot)\) n/a 97792 128
28900.2.es \(\chi_{28900}(21, \cdot)\) n/a 98048 128
28900.2.ev \(\chi_{28900}(67, \cdot)\) n/a 587008 128
28900.2.ew \(\chi_{28900}(183, \cdot)\) n/a 587008 128
28900.2.ey \(\chi_{28900}(121, \cdot)\) n/a 195584 256
28900.2.fb \(\chi_{28900}(87, \cdot)\) n/a 1174016 256
28900.2.fc \(\chi_{28900}(83, \cdot)\) n/a 1174016 256
28900.2.ff \(\chi_{28900}(9, \cdot)\) n/a 196096 256
28900.2.fh \(\chi_{28900}(73, \cdot)\) n/a 391680 512
28900.2.fj \(\chi_{28900}(11, \cdot)\) n/a 2348032 512
28900.2.fk \(\chi_{28900}(39, \cdot)\) n/a 2348032 512
28900.2.fm \(\chi_{28900}(37, \cdot)\) n/a 391680 512

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(28900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(28900)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(850))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1445))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2890))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5780))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14450))\)\(^{\oplus 2}\)