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Properties

Label 6075.2
Level 6075
Weight 2
Dimension 951648
Nonzero newspaces 30
Sturm bound 5248800

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Defining parameters

Level: \( N \) = \( 6075 = 3^{5} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(5248800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6075))\).

Total New Old
Modular forms 1322784 959520 363264
Cusp forms 1301617 951648 349969
Eisenstein series 21167 7872 13295

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6075))\)

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
6075.2.a \(\chi_{6075}(1, \cdot)\) 6075.2.a.a 1 1
6075.2.a.b 1
6075.2.a.c 1
6075.2.a.d 1
6075.2.a.e 1
6075.2.a.f 1
6075.2.a.g 1
6075.2.a.h 1
6075.2.a.i 1
6075.2.a.j 1
6075.2.a.k 1
6075.2.a.l 1
6075.2.a.m 1
6075.2.a.n 1
6075.2.a.o 1
6075.2.a.p 1
6075.2.a.q 1
6075.2.a.r 1
6075.2.a.s 1
6075.2.a.t 1
6075.2.a.u 1
6075.2.a.v 1
6075.2.a.w 1
6075.2.a.x 1
6075.2.a.y 1
6075.2.a.z 1
6075.2.a.ba 1
6075.2.a.bb 1
6075.2.a.bc 1
6075.2.a.bd 1
6075.2.a.be 1
6075.2.a.bf 1
6075.2.a.bg 1
6075.2.a.bh 1
6075.2.a.bi 1
6075.2.a.bj 1
6075.2.a.bk 2
6075.2.a.bl 2
6075.2.a.bm 2
6075.2.a.bn 2
6075.2.a.bo 2
6075.2.a.bp 2
6075.2.a.bq 3
6075.2.a.br 3
6075.2.a.bs 3
6075.2.a.bt 3
6075.2.a.bu 3
6075.2.a.bv 3
6075.2.a.bw 4
6075.2.a.bx 4
6075.2.a.by 4
6075.2.a.bz 4
6075.2.a.ca 4
6075.2.a.cb 4
6075.2.a.cc 6
6075.2.a.cd 6
6075.2.a.ce 6
6075.2.a.cf 6
6075.2.a.cg 6
6075.2.a.ch 6
6075.2.a.ci 6
6075.2.a.cj 6
6075.2.a.ck 9
6075.2.a.cl 9
6075.2.a.cm 12
6075.2.a.cn 12
6075.2.a.co 12
6075.2.a.cp 12
6075.2.a.cq 12
6075.2.a.cr 12
6075.2.b \(\chi_{6075}(2674, \cdot)\) n/a 216 1
6075.2.e \(\chi_{6075}(2026, \cdot)\) n/a 456 2
6075.2.f \(\chi_{6075}(1457, \cdot)\) n/a 432 2
6075.2.h \(\chi_{6075}(1216, \cdot)\) n/a 1440 4
6075.2.k \(\chi_{6075}(649, \cdot)\) n/a 432 2
6075.2.l \(\chi_{6075}(676, \cdot)\) n/a 1296 6
6075.2.n \(\chi_{6075}(244, \cdot)\) n/a 1440 4
6075.2.q \(\chi_{6075}(3482, \cdot)\) n/a 864 4
6075.2.r \(\chi_{6075}(406, \cdot)\) n/a 2880 8
6075.2.u \(\chi_{6075}(1324, \cdot)\) n/a 1248 6
6075.2.w \(\chi_{6075}(242, \cdot)\) n/a 2880 8
6075.2.x \(\chi_{6075}(226, \cdot)\) n/a 3024 18
6075.2.z \(\chi_{6075}(1054, \cdot)\) n/a 2880 8
6075.2.bb \(\chi_{6075}(107, \cdot)\) n/a 2496 12
6075.2.bd \(\chi_{6075}(136, \cdot)\) n/a 8448 24
6075.2.be \(\chi_{6075}(199, \cdot)\) n/a 2880 18
6075.2.bh \(\chi_{6075}(323, \cdot)\) n/a 5760 16
6075.2.bj \(\chi_{6075}(76, \cdot)\) n/a 27540 54
6075.2.bl \(\chi_{6075}(109, \cdot)\) n/a 8448 24
6075.2.bo \(\chi_{6075}(143, \cdot)\) n/a 5760 36
6075.2.bp \(\chi_{6075}(46, \cdot)\) n/a 19296 72
6075.2.br \(\chi_{6075}(49, \cdot)\) n/a 26136 54
6075.2.bt \(\chi_{6075}(53, \cdot)\) n/a 16896 48
6075.2.bv \(\chi_{6075}(19, \cdot)\) n/a 19296 72
6075.2.bz \(\chi_{6075}(32, \cdot)\) n/a 52272 108
6075.2.ca \(\chi_{6075}(16, \cdot)\) n/a 174528 216
6075.2.cc \(\chi_{6075}(8, \cdot)\) n/a 38592 144
6075.2.cf \(\chi_{6075}(4, \cdot)\) n/a 174528 216
6075.2.cg \(\chi_{6075}(2, \cdot)\) n/a 349056 432

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6075))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6075)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1215))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2025))\)\(^{\oplus 2}\)