Properties

Label 4005.2
Level 4005
Weight 2
Dimension 411366
Nonzero newspaces 56
Sturm bound 2280960

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Defining parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(2280960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4005))\).

Total New Old
Modular forms 575872 416066 159806
Cusp forms 564609 411366 153243
Eisenstein series 11263 4700 6563

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4005))\)

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
4005.2.a \(\chi_{4005}(1, \cdot)\) 4005.2.a.a 1 1
4005.2.a.b 1
4005.2.a.c 1
4005.2.a.d 1
4005.2.a.e 2
4005.2.a.f 2
4005.2.a.g 2
4005.2.a.h 2
4005.2.a.i 3
4005.2.a.j 3
4005.2.a.k 4
4005.2.a.l 4
4005.2.a.m 4
4005.2.a.n 6
4005.2.a.o 7
4005.2.a.p 8
4005.2.a.q 9
4005.2.a.r 10
4005.2.a.s 10
4005.2.a.t 10
4005.2.a.u 12
4005.2.a.v 12
4005.2.a.w 17
4005.2.a.x 17
4005.2.c \(\chi_{4005}(2404, \cdot)\) n/a 220 1
4005.2.e \(\chi_{4005}(2224, \cdot)\) n/a 224 1
4005.2.g \(\chi_{4005}(3826, \cdot)\) n/a 150 1
4005.2.i \(\chi_{4005}(1336, \cdot)\) n/a 704 2
4005.2.k \(\chi_{4005}(1369, \cdot)\) n/a 444 2
4005.2.l \(\chi_{4005}(233, \cdot)\) n/a 360 2
4005.2.n \(\chi_{4005}(2402, \cdot)\) n/a 360 2
4005.2.o \(\chi_{4005}(2582, \cdot)\) n/a 352 2
4005.2.r \(\chi_{4005}(2348, \cdot)\) n/a 360 2
4005.2.u \(\chi_{4005}(856, \cdot)\) n/a 300 2
4005.2.w \(\chi_{4005}(1156, \cdot)\) n/a 720 2
4005.2.y \(\chi_{4005}(889, \cdot)\) n/a 1072 2
4005.2.ba \(\chi_{4005}(1069, \cdot)\) n/a 1056 2
4005.2.bd \(\chi_{4005}(611, \cdot)\) n/a 480 4
4005.2.be \(\chi_{4005}(838, \cdot)\) n/a 892 4
4005.2.bf \(\chi_{4005}(37, \cdot)\) n/a 892 4
4005.2.bj \(\chi_{4005}(764, \cdot)\) n/a 720 4
4005.2.bk \(\chi_{4005}(91, \cdot)\) n/a 1500 10
4005.2.bl \(\chi_{4005}(301, \cdot)\) n/a 1440 4
4005.2.bo \(\chi_{4005}(767, \cdot)\) n/a 2144 4
4005.2.br \(\chi_{4005}(713, \cdot)\) n/a 2112 4
4005.2.bs \(\chi_{4005}(533, \cdot)\) n/a 2144 4
4005.2.bu \(\chi_{4005}(212, \cdot)\) n/a 2144 4
4005.2.bv \(\chi_{4005}(34, \cdot)\) n/a 2144 4
4005.2.by \(\chi_{4005}(406, \cdot)\) n/a 1500 10
4005.2.ca \(\chi_{4005}(289, \cdot)\) n/a 2240 10
4005.2.cc \(\chi_{4005}(64, \cdot)\) n/a 2240 10
4005.2.ce \(\chi_{4005}(344, \cdot)\) n/a 4288 8
4005.2.ci \(\chi_{4005}(457, \cdot)\) n/a 4288 8
4005.2.cj \(\chi_{4005}(52, \cdot)\) n/a 4288 8
4005.2.ck \(\chi_{4005}(101, \cdot)\) n/a 2880 8
4005.2.cm \(\chi_{4005}(16, \cdot)\) n/a 7200 20
4005.2.cn \(\chi_{4005}(136, \cdot)\) n/a 3000 20
4005.2.cq \(\chi_{4005}(53, \cdot)\) n/a 3600 20
4005.2.ct \(\chi_{4005}(8, \cdot)\) n/a 3600 20
4005.2.cu \(\chi_{4005}(278, \cdot)\) n/a 3600 20
4005.2.cw \(\chi_{4005}(17, \cdot)\) n/a 3600 20
4005.2.cx \(\chi_{4005}(109, \cdot)\) n/a 4440 20
4005.2.da \(\chi_{4005}(4, \cdot)\) n/a 10720 20
4005.2.dc \(\chi_{4005}(139, \cdot)\) n/a 10720 20
4005.2.de \(\chi_{4005}(526, \cdot)\) n/a 7200 20
4005.2.dg \(\chi_{4005}(224, \cdot)\) n/a 7200 40
4005.2.dk \(\chi_{4005}(28, \cdot)\) n/a 8920 40
4005.2.dl \(\chi_{4005}(82, \cdot)\) n/a 8920 40
4005.2.dm \(\chi_{4005}(26, \cdot)\) n/a 4800 40
4005.2.dp \(\chi_{4005}(49, \cdot)\) n/a 21440 40
4005.2.dq \(\chi_{4005}(47, \cdot)\) n/a 21440 40
4005.2.ds \(\chi_{4005}(203, \cdot)\) n/a 21440 40
4005.2.dt \(\chi_{4005}(2, \cdot)\) n/a 21440 40
4005.2.dw \(\chi_{4005}(68, \cdot)\) n/a 21440 40
4005.2.dz \(\chi_{4005}(106, \cdot)\) n/a 14400 40
4005.2.eb \(\chi_{4005}(41, \cdot)\) n/a 28800 80
4005.2.ec \(\chi_{4005}(43, \cdot)\) n/a 42880 80
4005.2.ed \(\chi_{4005}(7, \cdot)\) n/a 42880 80
4005.2.eh \(\chi_{4005}(14, \cdot)\) n/a 42880 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(89))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(267))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(445))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(801))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1335))\)\(^{\oplus 2}\)