Properties

Label 4719.2
Level 4719
Weight 2
Dimension 589568
Nonzero newspaces 48
Sturm bound 3252480

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Defining parameters

Level: \( N \) = \( 4719 = 3 \cdot 11^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(3252480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4719))\).

Total New Old
Modular forms 820800 595752 225048
Cusp forms 805441 589568 215873
Eisenstein series 15359 6184 9175

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4719))\)

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
4719.2.a \(\chi_{4719}(1, \cdot)\) 4719.2.a.a 1 1
4719.2.a.b 1
4719.2.a.c 1
4719.2.a.d 1
4719.2.a.e 1
4719.2.a.f 1
4719.2.a.g 1
4719.2.a.h 1
4719.2.a.i 1
4719.2.a.j 1
4719.2.a.k 1
4719.2.a.l 1
4719.2.a.m 1
4719.2.a.n 2
4719.2.a.o 2
4719.2.a.p 2
4719.2.a.q 3
4719.2.a.r 3
4719.2.a.s 3
4719.2.a.t 3
4719.2.a.u 3
4719.2.a.v 3
4719.2.a.w 3
4719.2.a.x 4
4719.2.a.y 4
4719.2.a.z 4
4719.2.a.ba 5
4719.2.a.bb 5
4719.2.a.bc 5
4719.2.a.bd 5
4719.2.a.be 5
4719.2.a.bf 5
4719.2.a.bg 6
4719.2.a.bh 6
4719.2.a.bi 10
4719.2.a.bj 10
4719.2.a.bk 10
4719.2.a.bl 10
4719.2.a.bm 10
4719.2.a.bn 10
4719.2.a.bo 14
4719.2.a.bp 14
4719.2.a.bq 18
4719.2.a.br 18
4719.2.b \(\chi_{4719}(727, \cdot)\) n/a 254 1
4719.2.e \(\chi_{4719}(4718, \cdot)\) n/a 488 1
4719.2.f \(\chi_{4719}(3992, \cdot)\) n/a 432 1
4719.2.i \(\chi_{4719}(1816, \cdot)\) n/a 510 2
4719.2.j \(\chi_{4719}(122, \cdot)\) n/a 980 2
4719.2.m \(\chi_{4719}(967, \cdot)\) n/a 504 2
4719.2.n \(\chi_{4719}(1600, \cdot)\) n/a 864 4
4719.2.p \(\chi_{4719}(1088, \cdot)\) n/a 976 2
4719.2.s \(\chi_{4719}(1453, \cdot)\) n/a 506 2
4719.2.t \(\chi_{4719}(725, \cdot)\) n/a 976 2
4719.2.x \(\chi_{4719}(1613, \cdot)\) n/a 1728 4
4719.2.y \(\chi_{4719}(233, \cdot)\) n/a 1952 4
4719.2.bb \(\chi_{4719}(493, \cdot)\) n/a 1008 4
4719.2.bc \(\chi_{4719}(430, \cdot)\) n/a 2640 10
4719.2.be \(\chi_{4719}(241, \cdot)\) n/a 1008 4
4719.2.bf \(\chi_{4719}(1211, \cdot)\) n/a 1964 4
4719.2.bh \(\chi_{4719}(874, \cdot)\) n/a 2016 8
4719.2.bj \(\chi_{4719}(632, \cdot)\) n/a 3904 8
4719.2.bk \(\chi_{4719}(112, \cdot)\) n/a 2016 8
4719.2.bo \(\chi_{4719}(131, \cdot)\) n/a 5280 10
4719.2.bp \(\chi_{4719}(428, \cdot)\) n/a 6120 10
4719.2.bs \(\chi_{4719}(298, \cdot)\) n/a 3080 10
4719.2.bu \(\chi_{4719}(524, \cdot)\) n/a 3904 8
4719.2.bv \(\chi_{4719}(511, \cdot)\) n/a 2016 8
4719.2.by \(\chi_{4719}(887, \cdot)\) n/a 3904 8
4719.2.ca \(\chi_{4719}(100, \cdot)\) n/a 6160 20
4719.2.cb \(\chi_{4719}(109, \cdot)\) n/a 6160 20
4719.2.ce \(\chi_{4719}(320, \cdot)\) n/a 12240 20
4719.2.cf \(\chi_{4719}(157, \cdot)\) n/a 10560 40
4719.2.cg \(\chi_{4719}(457, \cdot)\) n/a 4032 16
4719.2.cj \(\chi_{4719}(245, \cdot)\) n/a 7808 16
4719.2.cl \(\chi_{4719}(296, \cdot)\) n/a 12240 20
4719.2.cm \(\chi_{4719}(166, \cdot)\) n/a 6160 20
4719.2.cp \(\chi_{4719}(230, \cdot)\) n/a 12240 20
4719.2.cr \(\chi_{4719}(25, \cdot)\) n/a 12320 40
4719.2.cu \(\chi_{4719}(116, \cdot)\) n/a 24480 40
4719.2.cv \(\chi_{4719}(248, \cdot)\) n/a 21120 40
4719.2.cz \(\chi_{4719}(89, \cdot)\) n/a 24480 40
4719.2.da \(\chi_{4719}(76, \cdot)\) n/a 12320 40
4719.2.dc \(\chi_{4719}(16, \cdot)\) n/a 24640 80
4719.2.de \(\chi_{4719}(73, \cdot)\) n/a 24640 80
4719.2.df \(\chi_{4719}(5, \cdot)\) n/a 48960 80
4719.2.di \(\chi_{4719}(29, \cdot)\) n/a 48960 80
4719.2.dl \(\chi_{4719}(4, \cdot)\) n/a 24640 80
4719.2.dm \(\chi_{4719}(17, \cdot)\) n/a 48960 80
4719.2.do \(\chi_{4719}(20, \cdot)\) n/a 97920 160
4719.2.dr \(\chi_{4719}(7, \cdot)\) n/a 49280 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4719))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4719)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1573))\)\(^{\oplus 2}\)