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Properties

Label 8100.2
Level 8100
Weight 2
Dimension 740936
Nonzero newspaces 48
Sturm bound 6998400

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Defining parameters

Level: \( N \) = \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(6998400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8100))\).

Total New Old
Modular forms 1764720 745528 1019192
Cusp forms 1734481 740936 993545
Eisenstein series 30239 4592 25647

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8100))\)

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
8100.2.a \(\chi_{8100}(1, \cdot)\) 8100.2.a.a 1 1
8100.2.a.b 1
8100.2.a.c 1
8100.2.a.d 1
8100.2.a.e 1
8100.2.a.f 1
8100.2.a.g 1
8100.2.a.h 1
8100.2.a.i 1
8100.2.a.j 1
8100.2.a.k 1
8100.2.a.l 1
8100.2.a.m 1
8100.2.a.n 1
8100.2.a.o 2
8100.2.a.p 2
8100.2.a.q 2
8100.2.a.r 2
8100.2.a.s 2
8100.2.a.t 2
8100.2.a.u 3
8100.2.a.v 3
8100.2.a.w 4
8100.2.a.x 4
8100.2.a.y 4
8100.2.a.z 4
8100.2.a.ba 4
8100.2.a.bb 4
8100.2.a.bc 6
8100.2.a.bd 6
8100.2.a.be 8
8100.2.d \(\chi_{8100}(649, \cdot)\) 8100.2.d.a 2 1
8100.2.d.b 2
8100.2.d.c 2
8100.2.d.d 2
8100.2.d.e 2
8100.2.d.f 2
8100.2.d.g 2
8100.2.d.h 2
8100.2.d.i 2
8100.2.d.j 2
8100.2.d.k 4
8100.2.d.l 4
8100.2.d.m 4
8100.2.d.n 4
8100.2.d.o 6
8100.2.d.p 6
8100.2.d.q 8
8100.2.d.r 8
8100.2.d.s 8
8100.2.e \(\chi_{8100}(7451, \cdot)\) n/a 444 1
8100.2.h \(\chi_{8100}(8099, \cdot)\) n/a 424 1
8100.2.i \(\chi_{8100}(2701, \cdot)\) n/a 152 2
8100.2.j \(\chi_{8100}(1457, \cdot)\) n/a 144 2
8100.2.k \(\chi_{8100}(2107, \cdot)\) n/a 848 2
8100.2.n \(\chi_{8100}(1621, \cdot)\) n/a 480 4
8100.2.o \(\chi_{8100}(2699, \cdot)\) n/a 856 2
8100.2.r \(\chi_{8100}(2051, \cdot)\) n/a 900 2
8100.2.s \(\chi_{8100}(3349, \cdot)\) n/a 144 2
8100.2.v \(\chi_{8100}(901, \cdot)\) n/a 342 6
8100.2.w \(\chi_{8100}(971, \cdot)\) n/a 2848 4
8100.2.x \(\chi_{8100}(2269, \cdot)\) n/a 480 4
8100.2.ba \(\chi_{8100}(1619, \cdot)\) n/a 2848 4
8100.2.bf \(\chi_{8100}(593, \cdot)\) n/a 288 4
8100.2.bg \(\chi_{8100}(1243, \cdot)\) n/a 1712 4
8100.2.bh \(\chi_{8100}(541, \cdot)\) n/a 960 8
8100.2.bk \(\chi_{8100}(899, \cdot)\) n/a 1920 6
8100.2.bm \(\chi_{8100}(1549, \cdot)\) n/a 324 6
8100.2.bn \(\chi_{8100}(251, \cdot)\) n/a 2016 6
8100.2.br \(\chi_{8100}(163, \cdot)\) n/a 5696 8
8100.2.bs \(\chi_{8100}(1133, \cdot)\) n/a 960 8
8100.2.bt \(\chi_{8100}(301, \cdot)\) n/a 3078 18
8100.2.bw \(\chi_{8100}(539, \cdot)\) n/a 5728 8
8100.2.bz \(\chi_{8100}(109, \cdot)\) n/a 960 8
8100.2.ca \(\chi_{8100}(431, \cdot)\) n/a 5728 8
8100.2.cc \(\chi_{8100}(307, \cdot)\) n/a 3840 12
8100.2.ce \(\chi_{8100}(557, \cdot)\) n/a 648 12
8100.2.cf \(\chi_{8100}(181, \cdot)\) n/a 2160 24
8100.2.ch \(\chi_{8100}(299, \cdot)\) n/a 17424 18
8100.2.cj \(\chi_{8100}(551, \cdot)\) n/a 18360 18
8100.2.cm \(\chi_{8100}(49, \cdot)\) n/a 2916 18
8100.2.cn \(\chi_{8100}(703, \cdot)\) n/a 11456 16
8100.2.co \(\chi_{8100}(53, \cdot)\) n/a 1920 16
8100.2.cs \(\chi_{8100}(71, \cdot)\) n/a 12864 24
8100.2.ct \(\chi_{8100}(289, \cdot)\) n/a 2160 24
8100.2.cv \(\chi_{8100}(179, \cdot)\) n/a 12864 24
8100.2.cy \(\chi_{8100}(257, \cdot)\) n/a 5832 36
8100.2.db \(\chi_{8100}(7, \cdot)\) n/a 34848 36
8100.2.dc \(\chi_{8100}(61, \cdot)\) n/a 19440 72
8100.2.dd \(\chi_{8100}(17, \cdot)\) n/a 4320 48
8100.2.df \(\chi_{8100}(127, \cdot)\) n/a 25728 48
8100.2.di \(\chi_{8100}(11, \cdot)\) n/a 116352 72
8100.2.dj \(\chi_{8100}(169, \cdot)\) n/a 19440 72
8100.2.dn \(\chi_{8100}(59, \cdot)\) n/a 116352 72
8100.2.do \(\chi_{8100}(67, \cdot)\) n/a 232704 144
8100.2.dr \(\chi_{8100}(77, \cdot)\) n/a 38880 144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8100)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 45}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(810))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1620))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2025))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4050))\)\(^{\oplus 2}\)