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Properties

Label 6272.2
Level 6272
Weight 2
Dimension 647688
Nonzero newspaces 40
Sturm bound 4816896

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Defining parameters

Level: \( N \) = \( 6272 = 2^{7} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(4816896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6272))\).

Total New Old
Modular forms 1213824 652344 561480
Cusp forms 1194625 647688 546937
Eisenstein series 19199 4656 14543

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6272))\)

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
6272.2.a \(\chi_{6272}(1, \cdot)\) 6272.2.a.a 1 1
6272.2.a.b 1
6272.2.a.c 1
6272.2.a.d 1
6272.2.a.e 1
6272.2.a.f 1
6272.2.a.g 1
6272.2.a.h 1
6272.2.a.i 2
6272.2.a.j 2
6272.2.a.k 2
6272.2.a.l 2
6272.2.a.m 2
6272.2.a.n 2
6272.2.a.o 2
6272.2.a.p 2
6272.2.a.q 2
6272.2.a.r 2
6272.2.a.s 2
6272.2.a.t 2
6272.2.a.u 3
6272.2.a.v 3
6272.2.a.w 3
6272.2.a.x 3
6272.2.a.y 4
6272.2.a.z 4
6272.2.a.ba 4
6272.2.a.bb 4
6272.2.a.bc 4
6272.2.a.bd 4
6272.2.a.be 4
6272.2.a.bf 4
6272.2.a.bg 4
6272.2.a.bh 4
6272.2.a.bi 4
6272.2.a.bj 4
6272.2.a.bk 4
6272.2.a.bl 4
6272.2.a.bm 4
6272.2.a.bn 4
6272.2.a.bo 4
6272.2.a.bp 4
6272.2.a.bq 4
6272.2.a.br 4
6272.2.a.bs 4
6272.2.a.bt 4
6272.2.a.bu 4
6272.2.a.bv 4
6272.2.a.bw 6
6272.2.a.bx 6
6272.2.a.by 6
6272.2.a.bz 6
6272.2.b \(\chi_{6272}(3137, \cdot)\) n/a 164 1
6272.2.e \(\chi_{6272}(3135, \cdot)\) n/a 160 1
6272.2.f \(\chi_{6272}(6271, \cdot)\) n/a 160 1
6272.2.i \(\chi_{6272}(1537, \cdot)\) n/a 320 2
6272.2.j \(\chi_{6272}(1567, \cdot)\) n/a 304 2
6272.2.m \(\chi_{6272}(1569, \cdot)\) n/a 308 2
6272.2.p \(\chi_{6272}(2175, \cdot)\) n/a 320 2
6272.2.q \(\chi_{6272}(1599, \cdot)\) n/a 320 2
6272.2.t \(\chi_{6272}(961, \cdot)\) n/a 320 2
6272.2.u \(\chi_{6272}(897, \cdot)\) n/a 1344 6
6272.2.v \(\chi_{6272}(785, \cdot)\) n/a 636 4
6272.2.y \(\chi_{6272}(783, \cdot)\) n/a 624 4
6272.2.ba \(\chi_{6272}(31, \cdot)\) n/a 608 4
6272.2.bb \(\chi_{6272}(2529, \cdot)\) n/a 608 4
6272.2.bf \(\chi_{6272}(895, \cdot)\) n/a 1344 6
6272.2.bg \(\chi_{6272}(447, \cdot)\) n/a 1344 6
6272.2.bj \(\chi_{6272}(449, \cdot)\) n/a 1344 6
6272.2.bk \(\chi_{6272}(393, \cdot)\) None 0 8
6272.2.bl \(\chi_{6272}(391, \cdot)\) None 0 8
6272.2.bo \(\chi_{6272}(513, \cdot)\) n/a 2688 12
6272.2.bq \(\chi_{6272}(177, \cdot)\) n/a 1248 8
6272.2.br \(\chi_{6272}(815, \cdot)\) n/a 1248 8
6272.2.bt \(\chi_{6272}(225, \cdot)\) n/a 2640 12
6272.2.bw \(\chi_{6272}(223, \cdot)\) n/a 2640 12
6272.2.bx \(\chi_{6272}(195, \cdot)\) n/a 10176 16
6272.2.ca \(\chi_{6272}(197, \cdot)\) n/a 10416 16
6272.2.cb \(\chi_{6272}(65, \cdot)\) n/a 2688 12
6272.2.ce \(\chi_{6272}(703, \cdot)\) n/a 2688 12
6272.2.cf \(\chi_{6272}(255, \cdot)\) n/a 2688 12
6272.2.ck \(\chi_{6272}(215, \cdot)\) None 0 16
6272.2.cl \(\chi_{6272}(361, \cdot)\) None 0 16
6272.2.cm \(\chi_{6272}(111, \cdot)\) n/a 5328 24
6272.2.cp \(\chi_{6272}(113, \cdot)\) n/a 5328 24
6272.2.cr \(\chi_{6272}(289, \cdot)\) n/a 5280 24
6272.2.cs \(\chi_{6272}(159, \cdot)\) n/a 5280 24
6272.2.cv \(\chi_{6272}(19, \cdot)\) n/a 20352 32
6272.2.cw \(\chi_{6272}(165, \cdot)\) n/a 20352 32
6272.2.cy \(\chi_{6272}(55, \cdot)\) None 0 48
6272.2.cz \(\chi_{6272}(57, \cdot)\) None 0 48
6272.2.dd \(\chi_{6272}(47, \cdot)\) n/a 10656 48
6272.2.de \(\chi_{6272}(81, \cdot)\) n/a 10656 48
6272.2.dh \(\chi_{6272}(29, \cdot)\) n/a 85824 96
6272.2.di \(\chi_{6272}(27, \cdot)\) n/a 85824 96
6272.2.dm \(\chi_{6272}(9, \cdot)\) None 0 96
6272.2.dn \(\chi_{6272}(87, \cdot)\) None 0 96
6272.2.do \(\chi_{6272}(37, \cdot)\) n/a 171648 192
6272.2.dr \(\chi_{6272}(3, \cdot)\) n/a 171648 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6272))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6272)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(896))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1568))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3136))\)\(^{\oplus 2}\)