Properties

Label 6012.2
Level 6012
Weight 2
Dimension 462118
Nonzero newspaces 16
Sturm bound 4015872

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(4015872\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6012))\).

Total New Old
Modular forms 1010608 465090 545518
Cusp forms 997329 462118 535211
Eisenstein series 13279 2972 10307

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6012))\)

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
6012.2.a \(\chi_{6012}(1, \cdot)\) 6012.2.a.a 2 1
6012.2.a.b 3
6012.2.a.c 3
6012.2.a.d 5
6012.2.a.e 5
6012.2.a.f 5
6012.2.a.g 7
6012.2.a.h 9
6012.2.a.i 9
6012.2.a.j 10
6012.2.a.k 10
6012.2.b \(\chi_{6012}(667, \cdot)\) n/a 418 1
6012.2.c \(\chi_{6012}(2339, \cdot)\) n/a 332 1
6012.2.h \(\chi_{6012}(3005, \cdot)\) 6012.2.h.a 56 1
6012.2.i \(\chi_{6012}(2005, \cdot)\) n/a 332 2
6012.2.j \(\chi_{6012}(1001, \cdot)\) n/a 336 2
6012.2.o \(\chi_{6012}(335, \cdot)\) n/a 1992 2
6012.2.p \(\chi_{6012}(2671, \cdot)\) n/a 2008 2
6012.2.q \(\chi_{6012}(181, \cdot)\) n/a 5740 82
6012.2.r \(\chi_{6012}(17, \cdot)\) n/a 4592 82
6012.2.w \(\chi_{6012}(107, \cdot)\) n/a 27552 82
6012.2.x \(\chi_{6012}(55, \cdot)\) n/a 34276 82
6012.2.y \(\chi_{6012}(25, \cdot)\) n/a 27552 164
6012.2.z \(\chi_{6012}(43, \cdot)\) n/a 164656 164
6012.2.ba \(\chi_{6012}(11, \cdot)\) n/a 164656 164
6012.2.bf \(\chi_{6012}(5, \cdot)\) n/a 27552 164

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6012))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(668))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1002))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1503))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2004))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3006))\)\(^{\oplus 2}\)