Properties

Label 4410.2
Level 4410
Weight 2
Dimension 117929
Nonzero newspaces 60
Sturm bound 2032128

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Defining parameters

Level: \( N \) = \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(2032128\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4410))\).

Total New Old
Modular forms 515712 117929 397783
Cusp forms 500353 117929 382424
Eisenstein series 15359 0 15359

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4410))\)

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
4410.2.a \(\chi_{4410}(1, \cdot)\) 4410.2.a.a 1 1
4410.2.a.b 1
4410.2.a.c 1
4410.2.a.d 1
4410.2.a.e 1
4410.2.a.f 1
4410.2.a.g 1
4410.2.a.h 1
4410.2.a.i 1
4410.2.a.j 1
4410.2.a.k 1
4410.2.a.l 1
4410.2.a.m 1
4410.2.a.n 1
4410.2.a.o 1
4410.2.a.p 1
4410.2.a.q 1
4410.2.a.r 1
4410.2.a.s 1
4410.2.a.t 1
4410.2.a.u 1
4410.2.a.v 1
4410.2.a.w 1
4410.2.a.x 1
4410.2.a.y 1
4410.2.a.z 1
4410.2.a.ba 1
4410.2.a.bb 1
4410.2.a.bc 1
4410.2.a.bd 1
4410.2.a.be 1
4410.2.a.bf 1
4410.2.a.bg 1
4410.2.a.bh 1
4410.2.a.bi 1
4410.2.a.bj 1
4410.2.a.bk 1
4410.2.a.bl 1
4410.2.a.bm 1
4410.2.a.bn 2
4410.2.a.bo 2
4410.2.a.bp 2
4410.2.a.bq 2
4410.2.a.br 2
4410.2.a.bs 2
4410.2.a.bt 2
4410.2.a.bu 2
4410.2.a.bv 2
4410.2.a.bw 2
4410.2.a.bx 2
4410.2.a.by 2
4410.2.a.bz 2
4410.2.a.ca 2
4410.2.b \(\chi_{4410}(881, \cdot)\) 4410.2.b.a 8 1
4410.2.b.b 8
4410.2.b.c 8
4410.2.b.d 8
4410.2.b.e 8
4410.2.b.f 8
4410.2.d \(\chi_{4410}(4409, \cdot)\) 4410.2.d.a 16 1
4410.2.d.b 16
4410.2.d.c 24
4410.2.d.d 24
4410.2.g \(\chi_{4410}(3529, \cdot)\) n/a 102 1
4410.2.i \(\chi_{4410}(3301, \cdot)\) n/a 320 2
4410.2.j \(\chi_{4410}(1471, \cdot)\) n/a 328 2
4410.2.k \(\chi_{4410}(361, \cdot)\) n/a 136 2
4410.2.l \(\chi_{4410}(961, \cdot)\) n/a 320 2
4410.2.m \(\chi_{4410}(197, \cdot)\) n/a 164 2
4410.2.p \(\chi_{4410}(1567, \cdot)\) n/a 200 2
4410.2.r \(\chi_{4410}(2579, \cdot)\) n/a 480 2
4410.2.t \(\chi_{4410}(3461, \cdot)\) n/a 320 2
4410.2.u \(\chi_{4410}(1549, \cdot)\) n/a 200 2
4410.2.z \(\chi_{4410}(589, \cdot)\) n/a 492 2
4410.2.ba \(\chi_{4410}(2419, \cdot)\) n/a 480 2
4410.2.be \(\chi_{4410}(521, \cdot)\) n/a 112 2
4410.2.bf \(\chi_{4410}(1469, \cdot)\) n/a 480 2
4410.2.bi \(\chi_{4410}(509, \cdot)\) n/a 480 2
4410.2.bk \(\chi_{4410}(1391, \cdot)\) n/a 320 2
4410.2.bl \(\chi_{4410}(2351, \cdot)\) n/a 320 2
4410.2.bo \(\chi_{4410}(1979, \cdot)\) n/a 160 2
4410.2.bq \(\chi_{4410}(79, \cdot)\) n/a 480 2
4410.2.bs \(\chi_{4410}(631, \cdot)\) n/a 576 6
4410.2.bu \(\chi_{4410}(1733, \cdot)\) n/a 960 4
4410.2.bw \(\chi_{4410}(1207, \cdot)\) n/a 400 4
4410.2.bx \(\chi_{4410}(607, \cdot)\) n/a 960 4
4410.2.ca \(\chi_{4410}(97, \cdot)\) n/a 960 4
4410.2.cb \(\chi_{4410}(1373, \cdot)\) n/a 984 4
4410.2.ce \(\chi_{4410}(263, \cdot)\) n/a 960 4
4410.2.cf \(\chi_{4410}(557, \cdot)\) n/a 320 4
4410.2.ch \(\chi_{4410}(313, \cdot)\) n/a 960 4
4410.2.cl \(\chi_{4410}(379, \cdot)\) n/a 840 6
4410.2.cm \(\chi_{4410}(629, \cdot)\) n/a 672 6
4410.2.co \(\chi_{4410}(251, \cdot)\) n/a 480 6
4410.2.cq \(\chi_{4410}(331, \cdot)\) n/a 2688 12
4410.2.cr \(\chi_{4410}(541, \cdot)\) n/a 1104 12
4410.2.cs \(\chi_{4410}(211, \cdot)\) n/a 2688 12
4410.2.ct \(\chi_{4410}(121, \cdot)\) n/a 2688 12
4410.2.cv \(\chi_{4410}(307, \cdot)\) n/a 1680 12
4410.2.cw \(\chi_{4410}(323, \cdot)\) n/a 1344 12
4410.2.cy \(\chi_{4410}(319, \cdot)\) n/a 4032 12
4410.2.dc \(\chi_{4410}(89, \cdot)\) n/a 1344 12
4410.2.dd \(\chi_{4410}(41, \cdot)\) n/a 2688 12
4410.2.dg \(\chi_{4410}(101, \cdot)\) n/a 2688 12
4410.2.di \(\chi_{4410}(479, \cdot)\) n/a 4032 12
4410.2.dj \(\chi_{4410}(209, \cdot)\) n/a 4032 12
4410.2.dm \(\chi_{4410}(341, \cdot)\) n/a 864 12
4410.2.do \(\chi_{4410}(499, \cdot)\) n/a 4032 12
4410.2.dr \(\chi_{4410}(169, \cdot)\) n/a 4032 12
4410.2.du \(\chi_{4410}(109, \cdot)\) n/a 1680 12
4410.2.dx \(\chi_{4410}(311, \cdot)\) n/a 2688 12
4410.2.dz \(\chi_{4410}(59, \cdot)\) n/a 4032 12
4410.2.ea \(\chi_{4410}(157, \cdot)\) n/a 8064 24
4410.2.ec \(\chi_{4410}(113, \cdot)\) n/a 8064 24
4410.2.ef \(\chi_{4410}(53, \cdot)\) n/a 2688 24
4410.2.eg \(\chi_{4410}(23, \cdot)\) n/a 8064 24
4410.2.ej \(\chi_{4410}(103, \cdot)\) n/a 8064 24
4410.2.ek \(\chi_{4410}(73, \cdot)\) n/a 3360 24
4410.2.en \(\chi_{4410}(13, \cdot)\) n/a 8064 24
4410.2.ep \(\chi_{4410}(317, \cdot)\) n/a 8064 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4410))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4410)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(882))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1470))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2205))\)\(^{\oplus 2}\)