Properties

Label 4018.2
Level 4018
Weight 2
Dimension 157800
Nonzero newspaces 32
Sturm bound 1975680

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Defining parameters

Level: \( N \) = \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(1975680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4018))\).

Total New Old
Modular forms 498720 157800 340920
Cusp forms 489121 157800 331321
Eisenstein series 9599 0 9599

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4018))\)

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
4018.2.a \(\chi_{4018}(1, \cdot)\) 4018.2.a.a 1 1
4018.2.a.b 1
4018.2.a.c 1
4018.2.a.d 1
4018.2.a.e 1
4018.2.a.f 1
4018.2.a.g 1
4018.2.a.h 1
4018.2.a.i 1
4018.2.a.j 1
4018.2.a.k 1
4018.2.a.l 1
4018.2.a.m 1
4018.2.a.n 1
4018.2.a.o 1
4018.2.a.p 1
4018.2.a.q 1
4018.2.a.r 1
4018.2.a.s 1
4018.2.a.t 2
4018.2.a.u 2
4018.2.a.v 2
4018.2.a.w 2
4018.2.a.x 2
4018.2.a.y 2
4018.2.a.z 2
4018.2.a.ba 2
4018.2.a.bb 2
4018.2.a.bc 2
4018.2.a.bd 3
4018.2.a.be 3
4018.2.a.bf 3
4018.2.a.bg 3
4018.2.a.bh 3
4018.2.a.bi 4
4018.2.a.bj 4
4018.2.a.bk 4
4018.2.a.bl 4
4018.2.a.bm 4
4018.2.a.bn 6
4018.2.a.bo 6
4018.2.a.bp 6
4018.2.a.bq 6
4018.2.a.br 10
4018.2.a.bs 10
4018.2.a.bt 10
4018.2.a.bu 10
4018.2.c \(\chi_{4018}(491, \cdot)\) n/a 144 1
4018.2.e \(\chi_{4018}(165, \cdot)\) n/a 264 2
4018.2.f \(\chi_{4018}(2059, \cdot)\) n/a 286 2
4018.2.h \(\chi_{4018}(1863, \cdot)\) n/a 576 4
4018.2.j \(\chi_{4018}(655, \cdot)\) n/a 280 2
4018.2.l \(\chi_{4018}(575, \cdot)\) n/a 1104 6
4018.2.n \(\chi_{4018}(489, \cdot)\) n/a 560 4
4018.2.o \(\chi_{4018}(687, \cdot)\) n/a 576 4
4018.2.s \(\chi_{4018}(1157, \cdot)\) n/a 560 4
4018.2.u \(\chi_{4018}(1065, \cdot)\) n/a 1176 6
4018.2.w \(\chi_{4018}(961, \cdot)\) n/a 1120 8
4018.2.y \(\chi_{4018}(197, \cdot)\) n/a 1144 8
4018.2.z \(\chi_{4018}(247, \cdot)\) n/a 2256 12
4018.2.ba \(\chi_{4018}(325, \cdot)\) n/a 1120 8
4018.2.bd \(\chi_{4018}(155, \cdot)\) n/a 2352 12
4018.2.bg \(\chi_{4018}(373, \cdot)\) n/a 1120 8
4018.2.bh \(\chi_{4018}(57, \cdot)\) n/a 4704 24
4018.2.bi \(\chi_{4018}(97, \cdot)\) n/a 2240 16
4018.2.bl \(\chi_{4018}(81, \cdot)\) n/a 2352 12
4018.2.bo \(\chi_{4018}(27, \cdot)\) n/a 4704 24
4018.2.bp \(\chi_{4018}(361, \cdot)\) n/a 2240 16
4018.2.bt \(\chi_{4018}(113, \cdot)\) n/a 4704 24
4018.2.bu \(\chi_{4018}(9, \cdot)\) n/a 4704 24
4018.2.bw \(\chi_{4018}(37, \cdot)\) n/a 9408 48
4018.2.by \(\chi_{4018}(19, \cdot)\) n/a 4480 32
4018.2.bz \(\chi_{4018}(43, \cdot)\) n/a 9408 48
4018.2.cb \(\chi_{4018}(3, \cdot)\) n/a 9408 48
4018.2.cd \(\chi_{4018}(23, \cdot)\) n/a 9408 48
4018.2.cg \(\chi_{4018}(13, \cdot)\) n/a 18816 96
4018.2.cj \(\chi_{4018}(39, \cdot)\) n/a 18816 96
4018.2.cl \(\chi_{4018}(17, \cdot)\) n/a 37632 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4018))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4018)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(574))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2009))\)\(^{\oplus 2}\)