Properties

Label 8013.2
Level 8013
Weight 2
Dimension 1780889
Nonzero newspaces 16
Sturm bound 9512320

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Defining parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(9512320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8013))\).

Total New Old
Modular forms 2383420 1786229 597191
Cusp forms 2372741 1780889 591852
Eisenstein series 10679 5340 5339

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8013))\)

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
8013.2.a \(\chi_{8013}(1, \cdot)\) 8013.2.a.a 94 1
8013.2.a.b 106
8013.2.a.c 116
8013.2.a.d 129
8013.2.b \(\chi_{8013}(8012, \cdot)\) n/a 888 1
8013.2.e \(\chi_{8013}(544, \cdot)\) n/a 890 2
8013.2.f \(\chi_{8013}(2575, \cdot)\) n/a 1784 4
8013.2.h \(\chi_{8013}(545, \cdot)\) n/a 1778 2
8013.2.l \(\chi_{8013}(473, \cdot)\) n/a 3552 4
8013.2.m \(\chi_{8013}(37, \cdot)\) n/a 3560 8
8013.2.o \(\chi_{8013}(881, \cdot)\) n/a 7112 8
8013.2.q \(\chi_{8013}(490, \cdot)\) n/a 39248 88
8013.2.t \(\chi_{8013}(104, \cdot)\) n/a 78144 88
8013.2.u \(\chi_{8013}(40, \cdot)\) n/a 78320 176
8013.2.v \(\chi_{8013}(4, \cdot)\) n/a 156992 352
8013.2.x \(\chi_{8013}(62, \cdot)\) n/a 156464 176
8013.2.z \(\chi_{8013}(11, \cdot)\) n/a 312576 352
8013.2.bc \(\chi_{8013}(10, \cdot)\) n/a 313280 704
8013.2.be \(\chi_{8013}(14, \cdot)\) n/a 625856 704

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8013))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8013)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(2671))\)\(^{\oplus 2}\)