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Properties

Label 4056.2
Level 4056
Weight 2
Dimension 188567
Nonzero newspaces 36
Sturm bound 1817088

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Defining parameters

Level: \( N \) = \( 4056 = 2^{3} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(1817088\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4056))\).

Total New Old
Modular forms 459744 190203 269541
Cusp forms 448801 188567 260234
Eisenstein series 10943 1636 9307

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4056))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
4056.2.a \(\chi_{4056}(1, \cdot)\) 4056.2.a.a 1 1
4056.2.a.b 1
4056.2.a.c 1
4056.2.a.d 1
4056.2.a.e 1
4056.2.a.f 1
4056.2.a.g 1
4056.2.a.h 1
4056.2.a.i 1
4056.2.a.j 1
4056.2.a.k 1
4056.2.a.l 1
4056.2.a.m 1
4056.2.a.n 1
4056.2.a.o 1
4056.2.a.p 1
4056.2.a.q 1
4056.2.a.r 1
4056.2.a.s 1
4056.2.a.t 2
4056.2.a.u 2
4056.2.a.v 2
4056.2.a.w 2
4056.2.a.x 3
4056.2.a.y 3
4056.2.a.z 3
4056.2.a.ba 3
4056.2.a.bb 3
4056.2.a.bc 3
4056.2.a.bd 4
4056.2.a.be 4
4056.2.a.bf 6
4056.2.a.bg 6
4056.2.a.bh 6
4056.2.a.bi 6
4056.2.c \(\chi_{4056}(337, \cdot)\) 4056.2.c.a 2 1
4056.2.c.b 2
4056.2.c.c 2
4056.2.c.d 2
4056.2.c.e 2
4056.2.c.f 2
4056.2.c.g 2
4056.2.c.h 2
4056.2.c.i 2
4056.2.c.j 2
4056.2.c.k 4
4056.2.c.l 4
4056.2.c.m 6
4056.2.c.n 6
4056.2.c.o 6
4056.2.c.p 8
4056.2.c.q 12
4056.2.c.r 12
4056.2.d \(\chi_{4056}(3719, \cdot)\) None 0 1
4056.2.g \(\chi_{4056}(2029, \cdot)\) n/a 310 1
4056.2.h \(\chi_{4056}(2027, \cdot)\) n/a 596 1
4056.2.j \(\chi_{4056}(1691, \cdot)\) n/a 598 1
4056.2.m \(\chi_{4056}(2365, \cdot)\) n/a 308 1
4056.2.n \(\chi_{4056}(4055, \cdot)\) None 0 1
4056.2.q \(\chi_{4056}(529, \cdot)\) n/a 152 2
4056.2.t \(\chi_{4056}(2803, \cdot)\) n/a 616 2
4056.2.u \(\chi_{4056}(775, \cdot)\) None 0 2
4056.2.x \(\chi_{4056}(2465, \cdot)\) n/a 308 2
4056.2.y \(\chi_{4056}(437, \cdot)\) n/a 1192 2
4056.2.ba \(\chi_{4056}(1499, \cdot)\) n/a 1192 2
4056.2.bb \(\chi_{4056}(2005, \cdot)\) n/a 616 2
4056.2.be \(\chi_{4056}(191, \cdot)\) None 0 2
4056.2.bf \(\chi_{4056}(361, \cdot)\) n/a 156 2
4056.2.bj \(\chi_{4056}(23, \cdot)\) None 0 2
4056.2.bk \(\chi_{4056}(1837, \cdot)\) n/a 616 2
4056.2.bn \(\chi_{4056}(1667, \cdot)\) n/a 1192 2
4056.2.bo \(\chi_{4056}(1709, \cdot)\) n/a 2384 4
4056.2.bp \(\chi_{4056}(89, \cdot)\) n/a 616 4
4056.2.bs \(\chi_{4056}(319, \cdot)\) None 0 4
4056.2.bt \(\chi_{4056}(19, \cdot)\) n/a 1232 4
4056.2.bw \(\chi_{4056}(313, \cdot)\) n/a 1104 12
4056.2.bz \(\chi_{4056}(311, \cdot)\) None 0 12
4056.2.ca \(\chi_{4056}(181, \cdot)\) n/a 4368 12
4056.2.cd \(\chi_{4056}(131, \cdot)\) n/a 8688 12
4056.2.cf \(\chi_{4056}(155, \cdot)\) n/a 8688 12
4056.2.cg \(\chi_{4056}(157, \cdot)\) n/a 4368 12
4056.2.cj \(\chi_{4056}(287, \cdot)\) None 0 12
4056.2.ck \(\chi_{4056}(25, \cdot)\) n/a 1080 12
4056.2.cm \(\chi_{4056}(217, \cdot)\) n/a 2208 24
4056.2.cp \(\chi_{4056}(5, \cdot)\) n/a 17376 24
4056.2.cq \(\chi_{4056}(161, \cdot)\) n/a 4368 24
4056.2.ct \(\chi_{4056}(31, \cdot)\) None 0 24
4056.2.cu \(\chi_{4056}(187, \cdot)\) n/a 8736 24
4056.2.cv \(\chi_{4056}(35, \cdot)\) n/a 17376 24
4056.2.cy \(\chi_{4056}(205, \cdot)\) n/a 8736 24
4056.2.cz \(\chi_{4056}(95, \cdot)\) None 0 24
4056.2.dd \(\chi_{4056}(49, \cdot)\) n/a 2160 24
4056.2.de \(\chi_{4056}(263, \cdot)\) None 0 24
4056.2.dh \(\chi_{4056}(61, \cdot)\) n/a 8736 24
4056.2.di \(\chi_{4056}(179, \cdot)\) n/a 17376 24
4056.2.dk \(\chi_{4056}(67, \cdot)\) n/a 17472 48
4056.2.dl \(\chi_{4056}(7, \cdot)\) None 0 48
4056.2.do \(\chi_{4056}(41, \cdot)\) n/a 8736 48
4056.2.dp \(\chi_{4056}(149, \cdot)\) n/a 34752 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4056))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4056)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1014))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2028))\)\(^{\oplus 2}\)