Properties

Label 4704.2
Level 4704
Weight 2
Dimension 242786
Nonzero newspaces 48
Sturm bound 2408448

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Defining parameters

Level: \( N \) = \( 4704 = 2^{5} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(2408448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4704))\).

Total New Old
Modular forms 609792 244726 365066
Cusp forms 594433 242786 351647
Eisenstein series 15359 1940 13419

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4704))\)

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
4704.2.a \(\chi_{4704}(1, \cdot)\) 4704.2.a.a 1 1
4704.2.a.b 1
4704.2.a.c 1
4704.2.a.d 1
4704.2.a.e 1
4704.2.a.f 1
4704.2.a.g 1
4704.2.a.h 1
4704.2.a.i 1
4704.2.a.j 1
4704.2.a.k 1
4704.2.a.l 1
4704.2.a.m 1
4704.2.a.n 1
4704.2.a.o 1
4704.2.a.p 1
4704.2.a.q 1
4704.2.a.r 1
4704.2.a.s 1
4704.2.a.t 1
4704.2.a.u 1
4704.2.a.v 1
4704.2.a.w 1
4704.2.a.x 1
4704.2.a.y 1
4704.2.a.z 1
4704.2.a.ba 1
4704.2.a.bb 1
4704.2.a.bc 1
4704.2.a.bd 1
4704.2.a.be 1
4704.2.a.bf 1
4704.2.a.bg 1
4704.2.a.bh 1
4704.2.a.bi 2
4704.2.a.bj 2
4704.2.a.bk 2
4704.2.a.bl 2
4704.2.a.bm 2
4704.2.a.bn 2
4704.2.a.bo 2
4704.2.a.bp 2
4704.2.a.bq 2
4704.2.a.br 2
4704.2.a.bs 3
4704.2.a.bt 3
4704.2.a.bu 3
4704.2.a.bv 3
4704.2.a.bw 4
4704.2.a.bx 4
4704.2.a.by 4
4704.2.a.bz 4
4704.2.b \(\chi_{4704}(1567, \cdot)\) 4704.2.b.a 8 1
4704.2.b.b 8
4704.2.b.c 16
4704.2.b.d 16
4704.2.b.e 16
4704.2.b.f 16
4704.2.c \(\chi_{4704}(2353, \cdot)\) 4704.2.c.a 2 1
4704.2.c.b 4
4704.2.c.c 8
4704.2.c.d 12
4704.2.c.e 16
4704.2.c.f 16
4704.2.c.g 24
4704.2.h \(\chi_{4704}(4607, \cdot)\) n/a 164 1
4704.2.i \(\chi_{4704}(881, \cdot)\) n/a 152 1
4704.2.j \(\chi_{4704}(2255, \cdot)\) n/a 154 1
4704.2.k \(\chi_{4704}(3233, \cdot)\) n/a 160 1
4704.2.p \(\chi_{4704}(3919, \cdot)\) 4704.2.p.a 32 1
4704.2.p.b 48
4704.2.q \(\chi_{4704}(961, \cdot)\) n/a 160 2
4704.2.s \(\chi_{4704}(1079, \cdot)\) None 0 2
4704.2.u \(\chi_{4704}(391, \cdot)\) None 0 2
4704.2.w \(\chi_{4704}(1177, \cdot)\) None 0 2
4704.2.y \(\chi_{4704}(2057, \cdot)\) None 0 2
4704.2.bb \(\chi_{4704}(2383, \cdot)\) n/a 160 2
4704.2.bc \(\chi_{4704}(1697, \cdot)\) n/a 320 2
4704.2.bd \(\chi_{4704}(3215, \cdot)\) n/a 304 2
4704.2.bi \(\chi_{4704}(4049, \cdot)\) n/a 304 2
4704.2.bj \(\chi_{4704}(863, \cdot)\) n/a 320 2
4704.2.bk \(\chi_{4704}(3313, \cdot)\) n/a 160 2
4704.2.bl \(\chi_{4704}(31, \cdot)\) n/a 160 2
4704.2.bo \(\chi_{4704}(673, \cdot)\) n/a 672 6
4704.2.bp \(\chi_{4704}(293, \cdot)\) n/a 2528 4
4704.2.br \(\chi_{4704}(589, \cdot)\) n/a 1312 4
4704.2.bt \(\chi_{4704}(491, \cdot)\) n/a 2584 4
4704.2.bv \(\chi_{4704}(979, \cdot)\) n/a 1280 4
4704.2.bx \(\chi_{4704}(521, \cdot)\) None 0 4
4704.2.bz \(\chi_{4704}(361, \cdot)\) None 0 4
4704.2.cb \(\chi_{4704}(1207, \cdot)\) None 0 4
4704.2.cd \(\chi_{4704}(263, \cdot)\) None 0 4
4704.2.cf \(\chi_{4704}(559, \cdot)\) n/a 672 6
4704.2.ck \(\chi_{4704}(545, \cdot)\) n/a 1344 6
4704.2.cl \(\chi_{4704}(239, \cdot)\) n/a 1320 6
4704.2.cm \(\chi_{4704}(209, \cdot)\) n/a 1320 6
4704.2.cn \(\chi_{4704}(575, \cdot)\) n/a 1344 6
4704.2.cs \(\chi_{4704}(337, \cdot)\) n/a 672 6
4704.2.ct \(\chi_{4704}(223, \cdot)\) n/a 672 6
4704.2.cu \(\chi_{4704}(193, \cdot)\) n/a 1344 12
4704.2.cw \(\chi_{4704}(19, \cdot)\) n/a 2560 8
4704.2.cy \(\chi_{4704}(275, \cdot)\) n/a 5056 8
4704.2.da \(\chi_{4704}(373, \cdot)\) n/a 2560 8
4704.2.dc \(\chi_{4704}(509, \cdot)\) n/a 5056 8
4704.2.dd \(\chi_{4704}(41, \cdot)\) None 0 12
4704.2.df \(\chi_{4704}(169, \cdot)\) None 0 12
4704.2.dh \(\chi_{4704}(55, \cdot)\) None 0 12
4704.2.dj \(\chi_{4704}(71, \cdot)\) None 0 12
4704.2.dn \(\chi_{4704}(703, \cdot)\) n/a 1344 12
4704.2.do \(\chi_{4704}(529, \cdot)\) n/a 1344 12
4704.2.dp \(\chi_{4704}(95, \cdot)\) n/a 2688 12
4704.2.dq \(\chi_{4704}(17, \cdot)\) n/a 2640 12
4704.2.dv \(\chi_{4704}(431, \cdot)\) n/a 2640 12
4704.2.dw \(\chi_{4704}(257, \cdot)\) n/a 2688 12
4704.2.dx \(\chi_{4704}(271, \cdot)\) n/a 1344 12
4704.2.eb \(\chi_{4704}(155, \cdot)\) n/a 21408 24
4704.2.ed \(\chi_{4704}(139, \cdot)\) n/a 10752 24
4704.2.ef \(\chi_{4704}(125, \cdot)\) n/a 21408 24
4704.2.eh \(\chi_{4704}(85, \cdot)\) n/a 10752 24
4704.2.ej \(\chi_{4704}(23, \cdot)\) None 0 24
4704.2.el \(\chi_{4704}(103, \cdot)\) None 0 24
4704.2.en \(\chi_{4704}(25, \cdot)\) None 0 24
4704.2.ep \(\chi_{4704}(89, \cdot)\) None 0 24
4704.2.eq \(\chi_{4704}(37, \cdot)\) n/a 21504 48
4704.2.es \(\chi_{4704}(5, \cdot)\) n/a 42816 48
4704.2.eu \(\chi_{4704}(115, \cdot)\) n/a 21504 48
4704.2.ew \(\chi_{4704}(11, \cdot)\) n/a 42816 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4704))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4704)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(672))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1568))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2352))\)\(^{\oplus 2}\)