Properties

Label 4002.2
Level 4002
Weight 2
Dimension 110193
Nonzero newspaces 24
Sturm bound 1774080

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Defining parameters

Level: \( N \) = \( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(1774080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4002))\).

Total New Old
Modular forms 448448 110193 338255
Cusp forms 438593 110193 328400
Eisenstein series 9855 0 9855

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4002))\)

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
4002.2.a \(\chi_{4002}(1, \cdot)\) 4002.2.a.a 1 1
4002.2.a.b 1
4002.2.a.c 1
4002.2.a.d 1
4002.2.a.e 1
4002.2.a.f 1
4002.2.a.g 1
4002.2.a.h 1
4002.2.a.i 1
4002.2.a.j 1
4002.2.a.k 1
4002.2.a.l 1
4002.2.a.m 1
4002.2.a.n 1
4002.2.a.o 1
4002.2.a.p 1
4002.2.a.q 1
4002.2.a.r 1
4002.2.a.s 2
4002.2.a.t 2
4002.2.a.u 2
4002.2.a.v 2
4002.2.a.w 2
4002.2.a.x 2
4002.2.a.y 3
4002.2.a.z 3
4002.2.a.ba 4
4002.2.a.bb 4
4002.2.a.bc 4
4002.2.a.bd 4
4002.2.a.be 5
4002.2.a.bf 6
4002.2.a.bg 7
4002.2.a.bh 7
4002.2.a.bi 8
4002.2.a.bj 8
4002.2.a.bk 8
4002.2.f \(\chi_{4002}(4001, \cdot)\) n/a 240 1
4002.2.g \(\chi_{4002}(1103, \cdot)\) n/a 224 1
4002.2.h \(\chi_{4002}(2899, \cdot)\) n/a 108 1
4002.2.k \(\chi_{4002}(505, \cdot)\) n/a 240 2
4002.2.l \(\chi_{4002}(737, \cdot)\) n/a 440 2
4002.2.m \(\chi_{4002}(139, \cdot)\) n/a 672 6
4002.2.n \(\chi_{4002}(349, \cdot)\) n/a 1120 10
4002.2.o \(\chi_{4002}(415, \cdot)\) n/a 648 6
4002.2.p \(\chi_{4002}(413, \cdot)\) n/a 1440 6
4002.2.q \(\chi_{4002}(689, \cdot)\) n/a 1440 6
4002.2.v \(\chi_{4002}(289, \cdot)\) n/a 1200 10
4002.2.w \(\chi_{4002}(755, \cdot)\) n/a 2240 10
4002.2.x \(\chi_{4002}(521, \cdot)\) n/a 2400 10
4002.2.bc \(\chi_{4002}(47, \cdot)\) n/a 2640 12
4002.2.bd \(\chi_{4002}(229, \cdot)\) n/a 1440 12
4002.2.bg \(\chi_{4002}(41, \cdot)\) n/a 4800 20
4002.2.bh \(\chi_{4002}(157, \cdot)\) n/a 2400 20
4002.2.bk \(\chi_{4002}(25, \cdot)\) n/a 7200 60
4002.2.bp \(\chi_{4002}(5, \cdot)\) n/a 14400 60
4002.2.bq \(\chi_{4002}(53, \cdot)\) n/a 14400 60
4002.2.br \(\chi_{4002}(13, \cdot)\) n/a 7200 60
4002.2.bu \(\chi_{4002}(19, \cdot)\) n/a 14400 120
4002.2.bv \(\chi_{4002}(77, \cdot)\) n/a 28800 120

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(667))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1334))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2001))\)\(^{\oplus 2}\)