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Properties

Label 25050.2
Level 25050
Weight 2
Dimension 3855242
Nonzero newspaces 24
Sturm bound 66931200

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Defining parameters

Level: \( N \) = \( 25050 = 2 \cdot 3 \cdot 5^{2} \cdot 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(66931200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(25050))\).

Total New Old
Modular forms 16769984 3855242 12914742
Cusp forms 16695617 3855242 12840375
Eisenstein series 74367 0 74367

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(25050))\)

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
25050.2.a \(\chi_{25050}(1, \cdot)\) 25050.2.a.a 1 1
25050.2.a.b 1
25050.2.a.c 1
25050.2.a.d 1
25050.2.a.e 1
25050.2.a.f 1
25050.2.a.g 1
25050.2.a.h 1
25050.2.a.i 1
25050.2.a.j 1
25050.2.a.k 1
25050.2.a.l 1
25050.2.a.m 1
25050.2.a.n 1
25050.2.a.o 1
25050.2.a.p 1
25050.2.a.q 1
25050.2.a.r 1
25050.2.a.s 1
25050.2.a.t 1
25050.2.a.u 1
25050.2.a.v 1
25050.2.a.w 1
25050.2.a.x 1
25050.2.a.y 1
25050.2.a.z 1
25050.2.a.ba 1
25050.2.a.bb 2
25050.2.a.bc 2
25050.2.a.bd 2
25050.2.a.be 2
25050.2.a.bf 2
25050.2.a.bg 2
25050.2.a.bh 2
25050.2.a.bi 2
25050.2.a.bj 2
25050.2.a.bk 3
25050.2.a.bl 3
25050.2.a.bm 3
25050.2.a.bn 3
25050.2.a.bo 3
25050.2.a.bp 3
25050.2.a.bq 4
25050.2.a.br 4
25050.2.a.bs 4
25050.2.a.bt 4
25050.2.a.bu 5
25050.2.a.bv 5
25050.2.a.bw 5
25050.2.a.bx 5
25050.2.a.by 5
25050.2.a.bz 6
25050.2.a.ca 7
25050.2.a.cb 7
25050.2.a.cc 7
25050.2.a.cd 9
25050.2.a.ce 10
25050.2.a.cf 10
25050.2.a.cg 12
25050.2.a.ch 12
25050.2.a.ci 12
25050.2.a.cj 12
25050.2.a.ck 12
25050.2.a.cl 12
25050.2.a.cm 12
25050.2.a.cn 12
25050.2.a.co 14
25050.2.a.cp 14
25050.2.a.cq 15
25050.2.a.cr 15
25050.2.a.cs 15
25050.2.a.ct 15
25050.2.a.cu 16
25050.2.a.cv 16
25050.2.a.cw 16
25050.2.a.cx 16
25050.2.a.cy 16
25050.2.a.cz 16
25050.2.a.da 19
25050.2.a.db 19
25050.2.a.dc 24
25050.2.a.dd 24
25050.2.c \(\chi_{25050}(25049, \cdot)\) n/a 1008 1
25050.2.d \(\chi_{25050}(24049, \cdot)\) n/a 500 1
25050.2.f \(\chi_{25050}(1001, \cdot)\) n/a 1064 1
25050.2.i \(\chi_{25050}(4343, \cdot)\) n/a 1992 2
25050.2.k \(\chi_{25050}(13693, \cdot)\) n/a 1008 2
25050.2.m \(\chi_{25050}(5011, \cdot)\) n/a 3328 4
25050.2.o \(\chi_{25050}(4009, \cdot)\) n/a 3312 4
25050.2.p \(\chi_{25050}(5009, \cdot)\) n/a 6720 4
25050.2.t \(\chi_{25050}(6011, \cdot)\) n/a 6720 4
25050.2.v \(\chi_{25050}(667, \cdot)\) n/a 6720 8
25050.2.x \(\chi_{25050}(1337, \cdot)\) n/a 13280 8
25050.2.y \(\chi_{25050}(601, \cdot)\) n/a 43624 82
25050.2.bb \(\chi_{25050}(101, \cdot)\) n/a 87248 82
25050.2.bd \(\chi_{25050}(49, \cdot)\) n/a 41328 82
25050.2.be \(\chi_{25050}(149, \cdot)\) n/a 82656 82
25050.2.bh \(\chi_{25050}(43, \cdot)\) n/a 82656 164
25050.2.bj \(\chi_{25050}(107, \cdot)\) n/a 165312 164
25050.2.bk \(\chi_{25050}(31, \cdot)\) n/a 275520 328
25050.2.bl \(\chi_{25050}(41, \cdot)\) n/a 551040 328
25050.2.bp \(\chi_{25050}(59, \cdot)\) n/a 551040 328
25050.2.bq \(\chi_{25050}(19, \cdot)\) n/a 275520 328
25050.2.bs \(\chi_{25050}(47, \cdot)\) n/a 1102080 656
25050.2.bu \(\chi_{25050}(13, \cdot)\) n/a 551040 656

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(25050))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(25050)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(835))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1002))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1670))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2505))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5010))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12525))\)\(^{\oplus 2}\)