Properties

Label 4014.2
Level 4014
Weight 2
Dimension 118100
Nonzero newspaces 20
Sturm bound 1790208

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Defining parameters

Level: \( N \) = \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(1790208\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4014))\).

Total New Old
Modular forms 451104 118100 333004
Cusp forms 444001 118100 325901
Eisenstein series 7103 0 7103

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4014))\)

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
4014.2.a \(\chi_{4014}(1, \cdot)\) 4014.2.a.a 1 1
4014.2.a.b 1
4014.2.a.c 1
4014.2.a.d 1
4014.2.a.e 1
4014.2.a.f 1
4014.2.a.g 1
4014.2.a.h 1
4014.2.a.i 1
4014.2.a.j 2
4014.2.a.k 2
4014.2.a.l 2
4014.2.a.m 3
4014.2.a.n 3
4014.2.a.o 3
4014.2.a.p 3
4014.2.a.q 4
4014.2.a.r 5
4014.2.a.s 6
4014.2.a.t 6
4014.2.a.u 6
4014.2.a.v 7
4014.2.a.w 7
4014.2.a.x 8
4014.2.a.y 8
4014.2.a.z 8
4014.2.d \(\chi_{4014}(4013, \cdot)\) 4014.2.d.a 72 1
4014.2.e \(\chi_{4014}(1339, \cdot)\) n/a 444 2
4014.2.f \(\chi_{4014}(1075, \cdot)\) n/a 448 2
4014.2.g \(\chi_{4014}(2269, \cdot)\) n/a 188 2
4014.2.h \(\chi_{4014}(931, \cdot)\) n/a 448 2
4014.2.k \(\chi_{4014}(1337, \cdot)\) n/a 448 2
4014.2.l \(\chi_{4014}(407, \cdot)\) n/a 448 2
4014.2.m \(\chi_{4014}(1601, \cdot)\) n/a 152 2
4014.2.t \(\chi_{4014}(263, \cdot)\) n/a 448 2
4014.2.u \(\chi_{4014}(253, \cdot)\) n/a 3312 36
4014.2.v \(\chi_{4014}(125, \cdot)\) n/a 2592 36
4014.2.y \(\chi_{4014}(31, \cdot)\) n/a 16128 72
4014.2.z \(\chi_{4014}(19, \cdot)\) n/a 6768 72
4014.2.ba \(\chi_{4014}(25, \cdot)\) n/a 16128 72
4014.2.bb \(\chi_{4014}(7, \cdot)\) n/a 16128 72
4014.2.bc \(\chi_{4014}(11, \cdot)\) n/a 16128 72
4014.2.bj \(\chi_{4014}(35, \cdot)\) n/a 5472 72
4014.2.bk \(\chi_{4014}(5, \cdot)\) n/a 16128 72
4014.2.bl \(\chi_{4014}(59, \cdot)\) n/a 16128 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4014))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4014)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(223))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(446))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(669))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2007))\)\(^{\oplus 2}\)