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Properties

Label 39326.2
Level 39326
Weight 2
Dimension 15107274
Nonzero newspaces 24
Sturm bound 189304128

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Defining parameters

Level: \( N \) = \( 39326 = 2 \cdot 7 \cdot 53^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(189304128\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(39326))\).

Total New Old
Modular forms 47375328 15107274 32268054
Cusp forms 47276737 15107274 32169463
Eisenstein series 98591 0 98591

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(39326))\)

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
39326.2.a \(\chi_{39326}(1, \cdot)\) 39326.2.a.a 1 1
39326.2.a.b 1
39326.2.a.c 1
39326.2.a.d 1
39326.2.a.e 1
39326.2.a.f 1
39326.2.a.g 1
39326.2.a.h 1
39326.2.a.i 1
39326.2.a.j 1
39326.2.a.k 1
39326.2.a.l 1
39326.2.a.m 1
39326.2.a.n 1
39326.2.a.o 2
39326.2.a.p 2
39326.2.a.q 2
39326.2.a.r 3
39326.2.a.s 3
39326.2.a.t 3
39326.2.a.u 3
39326.2.a.v 3
39326.2.a.w 3
39326.2.a.x 3
39326.2.a.y 3
39326.2.a.z 3
39326.2.a.ba 3
39326.2.a.bb 4
39326.2.a.bc 4
39326.2.a.bd 5
39326.2.a.be 5
39326.2.a.bf 5
39326.2.a.bg 5
39326.2.a.bh 5
39326.2.a.bi 5
39326.2.a.bj 6
39326.2.a.bk 7
39326.2.a.bl 7
39326.2.a.bm 8
39326.2.a.bn 8
39326.2.a.bo 12
39326.2.a.bp 12
39326.2.a.bq 18
39326.2.a.br 18
39326.2.a.bs 18
39326.2.a.bt 18
39326.2.a.bu 21
39326.2.a.bv 21
39326.2.a.bw 36
39326.2.a.bx 36
39326.2.a.by 36
39326.2.a.bz 36
39326.2.a.ca 42
39326.2.a.cb 42
39326.2.a.cc 42
39326.2.a.cd 42
39326.2.a.ce 45
39326.2.a.cf 45
39326.2.a.cg 54
39326.2.a.ch 54
39326.2.a.ci 63
39326.2.a.cj 63
39326.2.a.ck 72
39326.2.a.cl 72
39326.2.a.cm 84
39326.2.a.cn 84
39326.2.a.co 84
39326.2.a.cp 84
39326.2.c \(\chi_{39326}(22471, \cdot)\) n/a 1376 1
39326.2.e \(\chi_{39326}(11237, \cdot)\) n/a 3672 2
39326.2.f \(\chi_{39326}(2309, \cdot)\) n/a 3672 2
39326.2.j \(\chi_{39326}(16853, \cdot)\) n/a 3672 2
39326.2.k \(\chi_{39326}(3309, \cdot)\) n/a 7344 4
39326.2.m \(\chi_{39326}(925, \cdot)\) n/a 16536 12
39326.2.o \(\chi_{39326}(5097, \cdot)\) n/a 16512 12
39326.2.q \(\chi_{39326}(1341, \cdot)\) n/a 44064 24
39326.2.s \(\chi_{39326}(4633, \cdot)\) n/a 44064 24
39326.2.t \(\chi_{39326}(743, \cdot)\) n/a 74360 52
39326.2.u \(\chi_{39326}(2349, \cdot)\) n/a 44064 24
39326.2.y \(\chi_{39326}(211, \cdot)\) n/a 74464 52
39326.2.bb \(\chi_{39326}(451, \cdot)\) n/a 88128 48
39326.2.bc \(\chi_{39326}(107, \cdot)\) n/a 198432 104
39326.2.be \(\chi_{39326}(83, \cdot)\) n/a 198432 104
39326.2.bf \(\chi_{39326}(317, \cdot)\) n/a 198432 104
39326.2.bj \(\chi_{39326}(129, \cdot)\) n/a 396864 208
39326.2.bk \(\chi_{39326}(15, \cdot)\) n/a 892320 624
39326.2.bm \(\chi_{39326}(29, \cdot)\) n/a 893568 624
39326.2.bo \(\chi_{39326}(81, \cdot)\) n/a 2381184 1248
39326.2.bp \(\chi_{39326}(27, \cdot)\) n/a 2381184 1248
39326.2.bt \(\chi_{39326}(9, \cdot)\) n/a 2381184 1248
39326.2.bu \(\chi_{39326}(3, \cdot)\) n/a 4762368 2496

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(39326))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(39326)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(106))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(371))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(742))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2809))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5618))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19663))\)\(^{\oplus 2}\)