Properties

Label 4010.2
Level 4010
Weight 2
Dimension 147401
Nonzero newspaces 30
Sturm bound 1929600

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Defining parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(1929600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4010))\).

Total New Old
Modular forms 485600 147401 338199
Cusp forms 479201 147401 331800
Eisenstein series 6399 0 6399

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4010))\)

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
4010.2.a \(\chi_{4010}(1, \cdot)\) 4010.2.a.a 1 1
4010.2.a.b 1
4010.2.a.c 1
4010.2.a.d 1
4010.2.a.e 1
4010.2.a.f 1
4010.2.a.g 2
4010.2.a.h 9
4010.2.a.i 10
4010.2.a.j 12
4010.2.a.k 15
4010.2.a.l 17
4010.2.a.m 20
4010.2.a.n 22
4010.2.a.o 22
4010.2.b \(\chi_{4010}(3209, \cdot)\) n/a 200 1
4010.2.c \(\chi_{4010}(801, \cdot)\) n/a 134 1
4010.2.d \(\chi_{4010}(4009, \cdot)\) n/a 200 1
4010.2.f \(\chi_{4010}(381, \cdot)\) n/a 268 2
4010.2.i \(\chi_{4010}(3589, \cdot)\) n/a 400 2
4010.2.k \(\chi_{4010}(841, \cdot)\) n/a 536 4
4010.2.m \(\chi_{4010}(1301, \cdot)\) n/a 536 4
4010.2.n \(\chi_{4010}(499, \cdot)\) n/a 808 4
4010.2.p \(\chi_{4010}(29, \cdot)\) n/a 800 4
4010.2.q \(\chi_{4010}(831, \cdot)\) n/a 536 4
4010.2.r \(\chi_{4010}(39, \cdot)\) n/a 800 4
4010.2.u \(\chi_{4010}(147, \cdot)\) n/a 1608 8
4010.2.v \(\chi_{4010}(133, \cdot)\) n/a 1608 8
4010.2.x \(\chi_{4010}(179, \cdot)\) n/a 1600 8
4010.2.ba \(\chi_{4010}(981, \cdot)\) n/a 1072 8
4010.2.bc \(\chi_{4010}(51, \cdot)\) n/a 2680 20
4010.2.be \(\chi_{4010}(239, \cdot)\) n/a 3232 16
4010.2.bf \(\chi_{4010}(151, \cdot)\) n/a 2144 16
4010.2.bh \(\chi_{4010}(629, \cdot)\) n/a 4000 20
4010.2.bi \(\chi_{4010}(41, \cdot)\) n/a 2680 20
4010.2.bj \(\chi_{4010}(489, \cdot)\) n/a 4000 20
4010.2.bm \(\chi_{4010}(153, \cdot)\) n/a 6432 32
4010.2.bn \(\chi_{4010}(33, \cdot)\) n/a 6432 32
4010.2.bo \(\chi_{4010}(81, \cdot)\) n/a 5360 40
4010.2.bp \(\chi_{4010}(49, \cdot)\) n/a 8000 40
4010.2.bu \(\chi_{4010}(11, \cdot)\) n/a 10720 80
4010.2.bv \(\chi_{4010}(9, \cdot)\) n/a 16160 80
4010.2.by \(\chi_{4010}(3, \cdot)\) n/a 32160 160
4010.2.bz \(\chi_{4010}(13, \cdot)\) n/a 32160 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4010))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4010)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(401))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(802))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2005))\)\(^{\oplus 2}\)