Properties

Label 6010.2
Level 6010
Weight 2
Dimension 331101
Nonzero newspaces 48
Sturm bound 4334400

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Defining parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(4334400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6010))\).

Total New Old
Modular forms 1088400 331101 757299
Cusp forms 1078801 331101 747700
Eisenstein series 9599 0 9599

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6010))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
6010.2.a \(\chi_{6010}(1, \cdot)\) 6010.2.a.a 1 1
6010.2.a.b 1
6010.2.a.c 16
6010.2.a.d 21
6010.2.a.e 21
6010.2.a.f 22
6010.2.a.g 27
6010.2.a.h 28
6010.2.a.i 29
6010.2.a.j 33
6010.2.b \(\chi_{6010}(4809, \cdot)\) n/a 300 1
6010.2.c \(\chi_{6010}(6009, \cdot)\) n/a 300 1
6010.2.d \(\chi_{6010}(1201, \cdot)\) n/a 198 1
6010.2.e \(\chi_{6010}(3581, \cdot)\) n/a 404 2
6010.2.f \(\chi_{6010}(2279, \cdot)\) n/a 604 2
6010.2.k \(\chi_{6010}(3481, \cdot)\) n/a 396 2
6010.2.l \(\chi_{6010}(4521, \cdot)\) n/a 792 4
6010.2.m \(\chi_{6010}(2981, \cdot)\) n/a 404 2
6010.2.n \(\chi_{6010}(1779, \cdot)\) n/a 600 2
6010.2.o \(\chi_{6010}(2379, \cdot)\) n/a 600 2
6010.2.q \(\chi_{6010}(163, \cdot)\) n/a 1204 4
6010.2.r \(\chi_{6010}(1143, \cdot)\) n/a 1204 4
6010.2.t \(\chi_{6010}(1371, \cdot)\) n/a 792 4
6010.2.u \(\chi_{6010}(169, \cdot)\) n/a 1200 4
6010.2.v \(\chi_{6010}(3319, \cdot)\) n/a 1200 4
6010.2.w \(\chi_{6010}(481, \cdot)\) n/a 808 4
6010.2.bb \(\chi_{6010}(2399, \cdot)\) n/a 1208 4
6010.2.bc \(\chi_{6010}(151, \cdot)\) n/a 1616 8
6010.2.bd \(\chi_{6010}(511, \cdot)\) n/a 1584 8
6010.2.bi \(\chi_{6010}(1189, \cdot)\) n/a 2416 8
6010.2.bk \(\chi_{6010}(387, \cdot)\) n/a 2408 8
6010.2.bl \(\chi_{6010}(273, \cdot)\) n/a 2408 8
6010.2.bn \(\chi_{6010}(301, \cdot)\) n/a 3960 20
6010.2.bo \(\chi_{6010}(619, \cdot)\) n/a 2400 8
6010.2.bp \(\chi_{6010}(199, \cdot)\) n/a 2400 8
6010.2.bq \(\chi_{6010}(1051, \cdot)\) n/a 1616 8
6010.2.bs \(\chi_{6010}(193, \cdot)\) n/a 4816 16
6010.2.bt \(\chi_{6010}(97, \cdot)\) n/a 4816 16
6010.2.bv \(\chi_{6010}(111, \cdot)\) n/a 3960 20
6010.2.bw \(\chi_{6010}(89, \cdot)\) n/a 6000 20
6010.2.bx \(\chi_{6010}(379, \cdot)\) n/a 6000 20
6010.2.by \(\chi_{6010}(289, \cdot)\) n/a 4832 16
6010.2.cd \(\chi_{6010}(441, \cdot)\) n/a 3232 16
6010.2.ce \(\chi_{6010}(81, \cdot)\) n/a 8080 40
6010.2.cf \(\chi_{6010}(119, \cdot)\) n/a 12080 40
6010.2.ck \(\chi_{6010}(101, \cdot)\) n/a 7920 40
6010.2.cm \(\chi_{6010}(87, \cdot)\) n/a 9632 32
6010.2.cn \(\chi_{6010}(17, \cdot)\) n/a 9632 32
6010.2.cp \(\chi_{6010}(651, \cdot)\) n/a 8080 40
6010.2.cq \(\chi_{6010}(9, \cdot)\) n/a 12000 40
6010.2.cr \(\chi_{6010}(179, \cdot)\) n/a 12000 40
6010.2.cs \(\chi_{6010}(123, \cdot)\) n/a 24080 80
6010.2.cv \(\chi_{6010}(63, \cdot)\) n/a 24080 80
6010.2.cw \(\chi_{6010}(39, \cdot)\) n/a 24160 80
6010.2.db \(\chi_{6010}(61, \cdot)\) n/a 16160 80
6010.2.dc \(\chi_{6010}(7, \cdot)\) n/a 48160 160
6010.2.df \(\chi_{6010}(33, \cdot)\) n/a 48160 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6010))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6010)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(601))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1202))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3005))\)\(^{\oplus 2}\)