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Properties

Label 9016.2
Level 9016
Weight 2
Dimension 1331506
Nonzero newspaces 48
Sturm bound 9934848

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Defining parameters

Level: \( N \) = \( 9016 = 2^{3} \cdot 7^{2} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(9934848\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9016))\).

Total New Old
Modular forms 2499552 1339654 1159898
Cusp forms 2467873 1331506 1136367
Eisenstein series 31679 8148 23531

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9016))\)

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
9016.2.a \(\chi_{9016}(1, \cdot)\) 9016.2.a.a 1 1
9016.2.a.b 1
9016.2.a.c 1
9016.2.a.d 1
9016.2.a.e 1
9016.2.a.f 1
9016.2.a.g 1
9016.2.a.h 1
9016.2.a.i 1
9016.2.a.j 1
9016.2.a.k 1
9016.2.a.l 1
9016.2.a.m 1
9016.2.a.n 1
9016.2.a.o 1
9016.2.a.p 2
9016.2.a.q 2
9016.2.a.r 2
9016.2.a.s 2
9016.2.a.t 2
9016.2.a.u 2
9016.2.a.v 2
9016.2.a.w 2
9016.2.a.x 2
9016.2.a.y 3
9016.2.a.z 3
9016.2.a.ba 4
9016.2.a.bb 4
9016.2.a.bc 4
9016.2.a.bd 4
9016.2.a.be 4
9016.2.a.bf 4
9016.2.a.bg 5
9016.2.a.bh 6
9016.2.a.bi 6
9016.2.a.bj 8
9016.2.a.bk 11
9016.2.a.bl 11
9016.2.a.bm 11
9016.2.a.bn 11
9016.2.a.bo 11
9016.2.a.bp 11
9016.2.a.bq 11
9016.2.a.br 11
9016.2.a.bs 14
9016.2.a.bt 18
9016.2.a.bu 18
9016.2.b \(\chi_{9016}(4509, \cdot)\) n/a 902 1
9016.2.e \(\chi_{9016}(1471, \cdot)\) None 0 1
9016.2.f \(\chi_{9016}(6761, \cdot)\) n/a 240 1
9016.2.i \(\chi_{9016}(5291, \cdot)\) n/a 880 1
9016.2.j \(\chi_{9016}(783, \cdot)\) None 0 1
9016.2.m \(\chi_{9016}(2253, \cdot)\) n/a 952 1
9016.2.n \(\chi_{9016}(5979, \cdot)\) n/a 974 1
9016.2.q \(\chi_{9016}(3313, \cdot)\) n/a 440 2
9016.2.s \(\chi_{9016}(275, \cdot)\) n/a 1904 2
9016.2.v \(\chi_{9016}(7773, \cdot)\) n/a 1904 2
9016.2.w \(\chi_{9016}(6303, \cdot)\) None 0 2
9016.2.z \(\chi_{9016}(1795, \cdot)\) n/a 1760 2
9016.2.ba \(\chi_{9016}(3265, \cdot)\) n/a 480 2
9016.2.bd \(\chi_{9016}(4783, \cdot)\) None 0 2
9016.2.be \(\chi_{9016}(7821, \cdot)\) n/a 1760 2
9016.2.bg \(\chi_{9016}(1289, \cdot)\) n/a 1848 6
9016.2.bh \(\chi_{9016}(393, \cdot)\) n/a 2460 10
9016.2.bk \(\chi_{9016}(827, \cdot)\) n/a 8040 6
9016.2.bl \(\chi_{9016}(965, \cdot)\) n/a 8040 6
9016.2.bo \(\chi_{9016}(2071, \cdot)\) None 0 6
9016.2.bp \(\chi_{9016}(139, \cdot)\) n/a 7392 6
9016.2.bs \(\chi_{9016}(321, \cdot)\) n/a 2016 6
9016.2.bt \(\chi_{9016}(183, \cdot)\) None 0 6
9016.2.bw \(\chi_{9016}(645, \cdot)\) n/a 7392 6
9016.2.bx \(\chi_{9016}(737, \cdot)\) n/a 3696 12
9016.2.ca \(\chi_{9016}(99, \cdot)\) n/a 9740 10
9016.2.cb \(\chi_{9016}(293, \cdot)\) n/a 9520 10
9016.2.ce \(\chi_{9016}(1175, \cdot)\) None 0 10
9016.2.cf \(\chi_{9016}(587, \cdot)\) n/a 9520 10
9016.2.ci \(\chi_{9016}(97, \cdot)\) n/a 2400 10
9016.2.cj \(\chi_{9016}(295, \cdot)\) None 0 10
9016.2.cm \(\chi_{9016}(197, \cdot)\) n/a 9740 10
9016.2.cn \(\chi_{9016}(177, \cdot)\) n/a 4800 20
9016.2.cp \(\chi_{9016}(93, \cdot)\) n/a 14784 12
9016.2.cq \(\chi_{9016}(919, \cdot)\) None 0 12
9016.2.ct \(\chi_{9016}(689, \cdot)\) n/a 4032 12
9016.2.cu \(\chi_{9016}(507, \cdot)\) n/a 14784 12
9016.2.cx \(\chi_{9016}(47, \cdot)\) None 0 12
9016.2.cy \(\chi_{9016}(45, \cdot)\) n/a 16080 12
9016.2.db \(\chi_{9016}(1563, \cdot)\) n/a 16080 12
9016.2.de \(\chi_{9016}(165, \cdot)\) n/a 19040 20
9016.2.df \(\chi_{9016}(79, \cdot)\) None 0 20
9016.2.di \(\chi_{9016}(129, \cdot)\) n/a 4800 20
9016.2.dj \(\chi_{9016}(2187, \cdot)\) n/a 19040 20
9016.2.dm \(\chi_{9016}(31, \cdot)\) None 0 20
9016.2.dn \(\chi_{9016}(1109, \cdot)\) n/a 19040 20
9016.2.dq \(\chi_{9016}(67, \cdot)\) n/a 19040 20
9016.2.ds \(\chi_{9016}(169, \cdot)\) n/a 20160 60
9016.2.dt \(\chi_{9016}(29, \cdot)\) n/a 80400 60
9016.2.dw \(\chi_{9016}(15, \cdot)\) None 0 60
9016.2.dx \(\chi_{9016}(153, \cdot)\) n/a 20160 60
9016.2.ea \(\chi_{9016}(27, \cdot)\) n/a 80400 60
9016.2.eb \(\chi_{9016}(55, \cdot)\) None 0 60
9016.2.ee \(\chi_{9016}(125, \cdot)\) n/a 80400 60
9016.2.ef \(\chi_{9016}(43, \cdot)\) n/a 80400 60
9016.2.ei \(\chi_{9016}(9, \cdot)\) n/a 40320 120
9016.2.ek \(\chi_{9016}(11, \cdot)\) n/a 160800 120
9016.2.en \(\chi_{9016}(5, \cdot)\) n/a 160800 120
9016.2.eo \(\chi_{9016}(87, \cdot)\) None 0 120
9016.2.er \(\chi_{9016}(3, \cdot)\) n/a 160800 120
9016.2.es \(\chi_{9016}(17, \cdot)\) n/a 40320 120
9016.2.ev \(\chi_{9016}(135, \cdot)\) None 0 120
9016.2.ew \(\chi_{9016}(261, \cdot)\) n/a 160800 120

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9016))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9016)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(644))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1127))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2254))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4508))\)\(^{\oplus 2}\)