Properties

Label 10000.2
Level 10000
Weight 2
Dimension 1551744
Nonzero newspaces 28
Sturm bound 12000000

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Defining parameters

Level: \( N \) = \( 10000 = 2^{4} \cdot 5^{4} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(12000000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(10000))\).

Total New Old
Modular forms 3015400 1558656 1456744
Cusp forms 2984601 1551744 1432857
Eisenstein series 30799 6912 23887

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(10000))\)

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
10000.2.a \(\chi_{10000}(1, \cdot)\) 10000.2.a.a 2 1
10000.2.a.b 2
10000.2.a.c 2
10000.2.a.d 2
10000.2.a.e 2
10000.2.a.f 2
10000.2.a.g 2
10000.2.a.h 2
10000.2.a.i 2
10000.2.a.j 2
10000.2.a.k 2
10000.2.a.l 2
10000.2.a.m 2
10000.2.a.n 2
10000.2.a.o 4
10000.2.a.p 4
10000.2.a.q 4
10000.2.a.r 4
10000.2.a.s 4
10000.2.a.t 4
10000.2.a.u 4
10000.2.a.v 4
10000.2.a.w 4
10000.2.a.x 4
10000.2.a.y 4
10000.2.a.z 4
10000.2.a.ba 4
10000.2.a.bb 4
10000.2.a.bc 6
10000.2.a.bd 6
10000.2.a.be 8
10000.2.a.bf 8
10000.2.a.bg 8
10000.2.a.bh 8
10000.2.a.bi 8
10000.2.a.bj 8
10000.2.a.bk 8
10000.2.a.bl 8
10000.2.a.bm 8
10000.2.a.bn 8
10000.2.a.bo 12
10000.2.a.bp 12
10000.2.a.bq 16
10000.2.a.br 16
10000.2.c \(\chi_{10000}(1249, \cdot)\) n/a 232 1
10000.2.d \(\chi_{10000}(5001, \cdot)\) None 0 1
10000.2.f \(\chi_{10000}(6249, \cdot)\) None 0 1
10000.2.j \(\chi_{10000}(443, \cdot)\) n/a 1888 2
10000.2.l \(\chi_{10000}(2501, \cdot)\) n/a 1888 2
10000.2.n \(\chi_{10000}(2943, \cdot)\) n/a 480 2
10000.2.o \(\chi_{10000}(807, \cdot)\) None 0 2
10000.2.q \(\chi_{10000}(3749, \cdot)\) n/a 1888 2
10000.2.s \(\chi_{10000}(3307, \cdot)\) n/a 1888 2
10000.2.u \(\chi_{10000}(2001, \cdot)\) n/a 936 4
10000.2.w \(\chi_{10000}(249, \cdot)\) None 0 4
10000.2.y \(\chi_{10000}(3249, \cdot)\) n/a 936 4
10000.2.bb \(\chi_{10000}(1001, \cdot)\) None 0 4
10000.2.bd \(\chi_{10000}(1307, \cdot)\) n/a 7584 8
10000.2.be \(\chi_{10000}(501, \cdot)\) n/a 7584 8
10000.2.bh \(\chi_{10000}(1943, \cdot)\) None 0 8
10000.2.bi \(\chi_{10000}(943, \cdot)\) n/a 1920 8
10000.2.bl \(\chi_{10000}(749, \cdot)\) n/a 7584 8
10000.2.bm \(\chi_{10000}(307, \cdot)\) n/a 7584 8
10000.2.bo \(\chi_{10000}(401, \cdot)\) n/a 4440 20
10000.2.br \(\chi_{10000}(201, \cdot)\) None 0 20
10000.2.bt \(\chi_{10000}(649, \cdot)\) None 0 20
10000.2.bu \(\chi_{10000}(49, \cdot)\) n/a 4440 20
10000.2.bx \(\chi_{10000}(149, \cdot)\) n/a 35760 40
10000.2.by \(\chi_{10000}(43, \cdot)\) n/a 35760 40
10000.2.cb \(\chi_{10000}(7, \cdot)\) None 0 40
10000.2.cc \(\chi_{10000}(143, \cdot)\) n/a 9000 40
10000.2.cf \(\chi_{10000}(107, \cdot)\) n/a 35760 40
10000.2.cg \(\chi_{10000}(101, \cdot)\) n/a 35760 40
10000.2.ci \(\chi_{10000}(81, \cdot)\) n/a 37400 100
10000.2.cl \(\chi_{10000}(41, \cdot)\) None 0 100
10000.2.cm \(\chi_{10000}(129, \cdot)\) n/a 37400 100
10000.2.cp \(\chi_{10000}(9, \cdot)\) None 0 100
10000.2.cq \(\chi_{10000}(29, \cdot)\) n/a 299600 200
10000.2.ct \(\chi_{10000}(67, \cdot)\) n/a 299600 200
10000.2.cu \(\chi_{10000}(3, \cdot)\) n/a 299600 200
10000.2.cx \(\chi_{10000}(23, \cdot)\) None 0 200
10000.2.cy \(\chi_{10000}(47, \cdot)\) n/a 75000 200
10000.2.da \(\chi_{10000}(21, \cdot)\) n/a 299600 200

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(10000))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(10000)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(500))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(625))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1000))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1250))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2000))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2500))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5000))\)\(^{\oplus 2}\)