Defining parameters

Level: \( N \) = \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(4967424\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6762))\).

Total New Old
Modular forms 1252416 296798 955618
Cusp forms 1231297 296798 934499
Eisenstein series 21119 0 21119

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6762))\)

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
6762.2.a \(\chi_{6762}(1, \cdot)\) 6762.2.a.a 1 1
6762.2.a.b 1
6762.2.a.c 1
6762.2.a.d 1
6762.2.a.e 1
6762.2.a.f 1
6762.2.a.g 1
6762.2.a.h 1
6762.2.a.i 1
6762.2.a.j 1
6762.2.a.k 1
6762.2.a.l 1
6762.2.a.m 1
6762.2.a.n 1
6762.2.a.o 1
6762.2.a.p 1
6762.2.a.q 1
6762.2.a.r 1
6762.2.a.s 1
6762.2.a.t 1
6762.2.a.u 1
6762.2.a.v 1
6762.2.a.w 1
6762.2.a.x 1
6762.2.a.y 1
6762.2.a.z 1
6762.2.a.ba 1
6762.2.a.bb 1
6762.2.a.bc 1
6762.2.a.bd 1
6762.2.a.be 1
6762.2.a.bf 1
6762.2.a.bg 1
6762.2.a.bh 1
6762.2.a.bi 1
6762.2.a.bj 1
6762.2.a.bk 1
6762.2.a.bl 1
6762.2.a.bm 1
6762.2.a.bn 1
6762.2.a.bo 2
6762.2.a.bp 2
6762.2.a.bq 2
6762.2.a.br 2
6762.2.a.bs 2
6762.2.a.bt 2
6762.2.a.bu 2
6762.2.a.bv 2
6762.2.a.bw 2
6762.2.a.bx 2
6762.2.a.by 2
6762.2.a.bz 2
6762.2.a.ca 2
6762.2.a.cb 2
6762.2.a.cc 2
6762.2.a.cd 2
6762.2.a.ce 3
6762.2.a.cf 3
6762.2.a.cg 4
6762.2.a.ch 4
6762.2.a.ci 4
6762.2.a.cj 4
6762.2.a.ck 4
6762.2.a.cl 4
6762.2.a.cm 4
6762.2.a.cn 4
6762.2.a.co 4
6762.2.a.cp 4
6762.2.a.cq 4
6762.2.a.cr 4
6762.2.a.cs 4
6762.2.a.ct 4
6762.2.a.cu 8
6762.2.a.cv 8
6762.2.f \(\chi_{6762}(5291, \cdot)\) n/a 296 1
6762.2.g \(\chi_{6762}(4507, \cdot)\) n/a 160 1
6762.2.h \(\chi_{6762}(3725, \cdot)\) n/a 328 1
6762.2.i \(\chi_{6762}(1243, \cdot)\) n/a 296 2
6762.2.j \(\chi_{6762}(275, \cdot)\) n/a 640 2
6762.2.k \(\chi_{6762}(1195, \cdot)\) n/a 320 2
6762.2.l \(\chi_{6762}(1979, \cdot)\) n/a 584 2
6762.2.q \(\chi_{6762}(967, \cdot)\) n/a 1248 6
6762.2.r \(\chi_{6762}(883, \cdot)\) n/a 1640 10
6762.2.s \(\chi_{6762}(827, \cdot)\) n/a 2688 6
6762.2.t \(\chi_{6762}(461, \cdot)\) n/a 2448 6
6762.2.u \(\chi_{6762}(643, \cdot)\) n/a 1344 6
6762.2.z \(\chi_{6762}(277, \cdot)\) n/a 2448 12
6762.2.ba \(\chi_{6762}(1079, \cdot)\) n/a 3280 10
6762.2.bb \(\chi_{6762}(97, \cdot)\) n/a 1600 10
6762.2.bc \(\chi_{6762}(587, \cdot)\) n/a 3200 10
6762.2.bh \(\chi_{6762}(361, \cdot)\) n/a 3200 20
6762.2.bm \(\chi_{6762}(229, \cdot)\) n/a 2688 12
6762.2.bn \(\chi_{6762}(47, \cdot)\) n/a 4944 12
6762.2.bo \(\chi_{6762}(137, \cdot)\) n/a 5376 12
6762.2.bt \(\chi_{6762}(215, \cdot)\) n/a 6400 20
6762.2.bu \(\chi_{6762}(19, \cdot)\) n/a 3200 20
6762.2.bv \(\chi_{6762}(263, \cdot)\) n/a 6400 20
6762.2.bw \(\chi_{6762}(85, \cdot)\) n/a 13440 60
6762.2.cb \(\chi_{6762}(181, \cdot)\) n/a 13440 60
6762.2.cc \(\chi_{6762}(41, \cdot)\) n/a 26880 60
6762.2.cd \(\chi_{6762}(113, \cdot)\) n/a 26880 60
6762.2.ce \(\chi_{6762}(25, \cdot)\) n/a 26880 120
6762.2.cf \(\chi_{6762}(11, \cdot)\) n/a 53760 120
6762.2.cg \(\chi_{6762}(59, \cdot)\) n/a 53760 120
6762.2.ch \(\chi_{6762}(61, \cdot)\) n/a 26880 120

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6762))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6762)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(483))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(966))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1127))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2254))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3381))\)\(^{\oplus 2}\)