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Properties

Label 31433.2
Level 31433
Weight 2
Dimension 40635580
Nonzero newspaces 40
Sturm bound 164013696

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Defining parameters

Level: \( N \) = \( 31433 = 17 \cdot 43^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(164013696\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(31433))\).

Total New Old
Modular forms 41046432 40713714 332718
Cusp forms 40960417 40635580 324837
Eisenstein series 86015 78134 7881

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(31433))\)

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
31433.2.a \(\chi_{31433}(1, \cdot)\) 31433.2.a.a 1 1
31433.2.a.b 1
31433.2.a.c 2
31433.2.a.d 4
31433.2.a.e 6
31433.2.a.f 8
31433.2.a.g 19
31433.2.a.h 21
31433.2.a.i 26
31433.2.a.j 26
31433.2.a.k 29
31433.2.a.l 29
31433.2.a.m 29
31433.2.a.n 29
31433.2.a.o 90
31433.2.a.p 90
31433.2.a.q 90
31433.2.a.r 90
31433.2.a.s 130
31433.2.a.t 130
31433.2.a.u 150
31433.2.a.v 150
31433.2.a.w 174
31433.2.a.x 174
31433.2.a.y 174
31433.2.a.z 174
31433.2.a.ba 260
31433.2.a.bb 300
31433.2.d \(\chi_{31433}(16642, \cdot)\) n/a 2666 1
31433.2.e \(\chi_{31433}(22611, \cdot)\) n/a 4812 2
31433.2.f \(\chi_{31433}(22189, \cdot)\) n/a 5332 2
31433.2.j \(\chi_{31433}(7819, \cdot)\) n/a 5332 2
31433.2.k \(\chi_{31433}(1208, \cdot)\) n/a 14424 6
31433.2.m \(\chi_{31433}(7397, \cdot)\) n/a 10668 4
31433.2.n \(\chi_{31433}(13366, \cdot)\) n/a 10664 4
31433.2.p \(\chi_{31433}(1546, \cdot)\) n/a 15996 6
31433.2.s \(\chi_{31433}(1848, \cdot)\) n/a 21328 8
31433.2.u \(\chi_{31433}(5271, \cdot)\) n/a 28872 12
31433.2.v \(\chi_{31433}(423, \cdot)\) n/a 21328 8
31433.2.y \(\chi_{31433}(4101, \cdot)\) n/a 31992 12
31433.2.z \(\chi_{31433}(3110, \cdot)\) n/a 31992 12
31433.2.bc \(\chi_{31433}(732, \cdot)\) n/a 106008 42
31433.2.be \(\chi_{31433}(2273, \cdot)\) n/a 42656 16
31433.2.bf \(\chi_{31433}(2252, \cdot)\) n/a 63984 24
31433.2.bi \(\chi_{31433}(361, \cdot)\) n/a 63984 24
31433.2.bj \(\chi_{31433}(560, \cdot)\) n/a 119112 42
31433.2.bn \(\chi_{31433}(75, \cdot)\) n/a 127968 48
31433.2.bo \(\chi_{31433}(307, \cdot)\) n/a 211848 84
31433.2.bq \(\chi_{31433}(1573, \cdot)\) n/a 127968 48
31433.2.bs \(\chi_{31433}(259, \cdot)\) n/a 238224 84
31433.2.bt \(\chi_{31433}(135, \cdot)\) n/a 238224 84
31433.2.bw \(\chi_{31433}(35, \cdot)\) n/a 636048 252
31433.2.bx \(\chi_{31433}(261, \cdot)\) n/a 255936 96
31433.2.bz \(\chi_{31433}(87, \cdot)\) n/a 476448 168
31433.2.cc \(\chi_{31433}(208, \cdot)\) n/a 476448 168
31433.2.cf \(\chi_{31433}(16, \cdot)\) n/a 714672 252
31433.2.ch \(\chi_{31433}(214, \cdot)\) n/a 952896 336
31433.2.ci \(\chi_{31433}(52, \cdot)\) n/a 1271088 504
31433.2.ck \(\chi_{31433}(36, \cdot)\) n/a 952896 336
31433.2.cl \(\chi_{31433}(4, \cdot)\) n/a 1429344 504
31433.2.cp \(\chi_{31433}(67, \cdot)\) n/a 1429344 504
31433.2.cq \(\chi_{31433}(7, \cdot)\) n/a 1905792 672
31433.2.ct \(\chi_{31433}(59, \cdot)\) n/a 2858688 1008
31433.2.cu \(\chi_{31433}(13, \cdot)\) n/a 2858688 1008
31433.2.cw \(\chi_{31433}(22, \cdot)\) n/a 5717376 2016
31433.2.cy \(\chi_{31433}(9, \cdot)\) n/a 5717376 2016
31433.2.db \(\chi_{31433}(3, \cdot)\) n/a 11434752 4032

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(31433))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(31433)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(731))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1849))\)\(^{\oplus 2}\)