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Properties

Label 8850.2
Level 8850
Weight 2
Dimension 480836
Nonzero newspaces 24
Sturm bound 8352000

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Defining parameters

Level: \( N \) = \( 8850 = 2 \cdot 3 \cdot 5^{2} \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(8352000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8850))\).

Total New Old
Modular forms 2100992 480836 1620156
Cusp forms 2075009 480836 1594173
Eisenstein series 25983 0 25983

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8850))\)

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
8850.2.a \(\chi_{8850}(1, \cdot)\) 8850.2.a.a 1 1
8850.2.a.b 1
8850.2.a.c 1
8850.2.a.d 1
8850.2.a.e 1
8850.2.a.f 1
8850.2.a.g 1
8850.2.a.h 1
8850.2.a.i 1
8850.2.a.j 1
8850.2.a.k 1
8850.2.a.l 1
8850.2.a.m 1
8850.2.a.n 1
8850.2.a.o 1
8850.2.a.p 1
8850.2.a.q 1
8850.2.a.r 1
8850.2.a.s 1
8850.2.a.t 1
8850.2.a.u 1
8850.2.a.v 1
8850.2.a.w 1
8850.2.a.x 1
8850.2.a.y 1
8850.2.a.z 1
8850.2.a.ba 1
8850.2.a.bb 1
8850.2.a.bc 1
8850.2.a.bd 1
8850.2.a.be 1
8850.2.a.bf 1
8850.2.a.bg 1
8850.2.a.bh 1
8850.2.a.bi 2
8850.2.a.bj 2
8850.2.a.bk 2
8850.2.a.bl 2
8850.2.a.bm 2
8850.2.a.bn 2
8850.2.a.bo 2
8850.2.a.bp 2
8850.2.a.bq 2
8850.2.a.br 2
8850.2.a.bs 2
8850.2.a.bt 3
8850.2.a.bu 3
8850.2.a.bv 3
8850.2.a.bw 3
8850.2.a.bx 3
8850.2.a.by 3
8850.2.a.bz 3
8850.2.a.ca 3
8850.2.a.cb 4
8850.2.a.cc 4
8850.2.a.cd 4
8850.2.a.ce 4
8850.2.a.cf 4
8850.2.a.cg 4
8850.2.a.ch 4
8850.2.a.ci 4
8850.2.a.cj 4
8850.2.a.ck 4
8850.2.a.cl 4
8850.2.a.cm 4
8850.2.a.cn 6
8850.2.a.co 6
8850.2.a.cp 6
8850.2.a.cq 6
8850.2.a.cr 7
8850.2.a.cs 7
8850.2.a.ct 9
8850.2.a.cu 9
8850.2.d \(\chi_{8850}(4249, \cdot)\) n/a 176 1
8850.2.e \(\chi_{8850}(8849, \cdot)\) n/a 360 1
8850.2.h \(\chi_{8850}(4601, \cdot)\) n/a 380 1
8850.2.i \(\chi_{8850}(943, \cdot)\) n/a 360 2
8850.2.j \(\chi_{8850}(2243, \cdot)\) n/a 696 2
8850.2.m \(\chi_{8850}(1771, \cdot)\) n/a 1168 4
8850.2.n \(\chi_{8850}(1769, \cdot)\) n/a 2400 4
8850.2.o \(\chi_{8850}(709, \cdot)\) n/a 1152 4
8850.2.r \(\chi_{8850}(1061, \cdot)\) n/a 2400 4
8850.2.w \(\chi_{8850}(473, \cdot)\) n/a 4640 8
8850.2.x \(\chi_{8850}(1297, \cdot)\) n/a 2400 8
8850.2.y \(\chi_{8850}(901, \cdot)\) n/a 5320 28
8850.2.z \(\chi_{8850}(101, \cdot)\) n/a 10640 28
8850.2.bc \(\chi_{8850}(149, \cdot)\) n/a 10080 28
8850.2.bd \(\chi_{8850}(49, \cdot)\) n/a 5040 28
8850.2.bi \(\chi_{8850}(107, \cdot)\) n/a 20160 56
8850.2.bj \(\chi_{8850}(43, \cdot)\) n/a 10080 56
8850.2.bk \(\chi_{8850}(121, \cdot)\) n/a 33600 112
8850.2.bn \(\chi_{8850}(11, \cdot)\) n/a 67200 112
8850.2.bq \(\chi_{8850}(19, \cdot)\) n/a 33600 112
8850.2.br \(\chi_{8850}(89, \cdot)\) n/a 67200 112
8850.2.bs \(\chi_{8850}(13, \cdot)\) n/a 67200 224
8850.2.bt \(\chi_{8850}(17, \cdot)\) n/a 134400 224

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8850))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8850)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(295))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(354))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(590))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(885))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1475))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1770))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2950))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4425))\)\(^{\oplus 2}\)