Properties

Label 6036.2
Level 6036
Weight 2
Dimension 441760
Nonzero newspaces 8
Sturm bound 4048128

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Defining parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(4048128\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6036))\).

Total New Old
Modular forms 1017052 443760 573292
Cusp forms 1007013 441760 565253
Eisenstein series 10039 2000 8039

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6036))\)

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
6036.2.a \(\chi_{6036}(1, \cdot)\) 6036.2.a.a 1 1
6036.2.a.b 1
6036.2.a.c 1
6036.2.a.d 1
6036.2.a.e 1
6036.2.a.f 14
6036.2.a.g 15
6036.2.a.h 24
6036.2.a.i 26
6036.2.b \(\chi_{6036}(2011, \cdot)\) n/a 504 1
6036.2.c \(\chi_{6036}(1007, \cdot)\) n/a 1004 1
6036.2.h \(\chi_{6036}(3017, \cdot)\) n/a 168 1
6036.2.i \(\chi_{6036}(13, \cdot)\) n/a 21000 250
6036.2.j \(\chi_{6036}(5, \cdot)\) n/a 42000 250
6036.2.o \(\chi_{6036}(11, \cdot)\) n/a 251000 250
6036.2.p \(\chi_{6036}(19, \cdot)\) n/a 126000 250

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6036))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6036)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(503))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1006))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1509))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2012))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3018))\)\(^{\oplus 2}\)