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Properties

Label 8619.2
Level 8619
Weight 2
Dimension 1999938
Nonzero newspaces 72
Sturm bound 10902528

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Defining parameters

Level: \( N \) = \( 8619 = 3 \cdot 13^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(10902528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8619))\).

Total New Old
Modular forms 2740224 2012210 728014
Cusp forms 2711041 1999938 711103
Eisenstein series 29183 12272 16911

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8619))\)

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
8619.2.a \(\chi_{8619}(1, \cdot)\) 8619.2.a.a 1 1
8619.2.a.b 1
8619.2.a.c 1
8619.2.a.d 1
8619.2.a.e 1
8619.2.a.f 1
8619.2.a.g 1
8619.2.a.h 1
8619.2.a.i 1
8619.2.a.j 1
8619.2.a.k 1
8619.2.a.l 1
8619.2.a.m 1
8619.2.a.n 1
8619.2.a.o 2
8619.2.a.p 2
8619.2.a.q 2
8619.2.a.r 3
8619.2.a.s 3
8619.2.a.t 3
8619.2.a.u 3
8619.2.a.v 4
8619.2.a.w 5
8619.2.a.x 5
8619.2.a.y 6
8619.2.a.z 6
8619.2.a.ba 6
8619.2.a.bb 6
8619.2.a.bc 6
8619.2.a.bd 8
8619.2.a.be 8
8619.2.a.bf 8
8619.2.a.bg 8
8619.2.a.bh 9
8619.2.a.bi 9
8619.2.a.bj 10
8619.2.a.bk 11
8619.2.a.bl 11
8619.2.a.bm 12
8619.2.a.bn 16
8619.2.a.bo 20
8619.2.a.bp 21
8619.2.a.bq 21
8619.2.a.br 22
8619.2.a.bs 24
8619.2.a.bt 24
8619.2.a.bu 24
8619.2.a.bv 24
8619.2.a.bw 24
8619.2.a.bx 24
8619.2.b \(\chi_{8619}(5407, \cdot)\) n/a 412 1
8619.2.e \(\chi_{8619}(2872, \cdot)\) n/a 464 1
8619.2.f \(\chi_{8619}(6085, \cdot)\) n/a 464 1
8619.2.i \(\chi_{8619}(3571, \cdot)\) n/a 820 2
8619.2.j \(\chi_{8619}(6592, \cdot)\) n/a 928 2
8619.2.m \(\chi_{8619}(6830, \cdot)\) n/a 1808 2
8619.2.n \(\chi_{8619}(239, \cdot)\) n/a 1640 2
8619.2.q \(\chi_{8619}(5507, \cdot)\) n/a 1808 2
8619.2.r \(\chi_{8619}(6014, \cdot)\) n/a 1808 2
8619.2.u \(\chi_{8619}(3379, \cdot)\) n/a 928 2
8619.2.w \(\chi_{8619}(1036, \cdot)\) n/a 920 2
8619.2.z \(\chi_{8619}(868, \cdot)\) n/a 820 2
8619.2.ba \(\chi_{8619}(6952, \cdot)\) n/a 928 2
8619.2.bd \(\chi_{8619}(746, \cdot)\) n/a 3616 4
8619.2.bg \(\chi_{8619}(508, \cdot)\) n/a 1864 4
8619.2.bh \(\chi_{8619}(1351, \cdot)\) n/a 1840 4
8619.2.bi \(\chi_{8619}(1760, \cdot)\) n/a 3616 4
8619.2.bk \(\chi_{8619}(361, \cdot)\) n/a 1856 4
8619.2.bm \(\chi_{8619}(89, \cdot)\) n/a 3616 4
8619.2.bp \(\chi_{8619}(5150, \cdot)\) n/a 3616 4
8619.2.bq \(\chi_{8619}(188, \cdot)\) n/a 3288 4
8619.2.bt \(\chi_{8619}(6065, \cdot)\) n/a 3616 4
8619.2.bv \(\chi_{8619}(1543, \cdot)\) n/a 1840 4
8619.2.bw \(\chi_{8619}(664, \cdot)\) n/a 5808 12
8619.2.by \(\chi_{8619}(1013, \cdot)\) n/a 7232 8
8619.2.bz \(\chi_{8619}(677, \cdot)\) n/a 7264 8
8619.2.cb \(\chi_{8619}(775, \cdot)\) n/a 3696 8
8619.2.ce \(\chi_{8619}(1591, \cdot)\) n/a 3696 8
8619.2.cg \(\chi_{8619}(587, \cdot)\) n/a 7232 8
8619.2.ch \(\chi_{8619}(484, \cdot)\) n/a 3712 8
8619.2.ci \(\chi_{8619}(1375, \cdot)\) n/a 3680 8
8619.2.cl \(\chi_{8619}(695, \cdot)\) n/a 7232 8
8619.2.cp \(\chi_{8619}(118, \cdot)\) n/a 6576 12
8619.2.cq \(\chi_{8619}(220, \cdot)\) n/a 6528 12
8619.2.ct \(\chi_{8619}(103, \cdot)\) n/a 5808 12
8619.2.cu \(\chi_{8619}(256, \cdot)\) n/a 11664 24
8619.2.cv \(\chi_{8619}(826, \cdot)\) n/a 7392 16
8619.2.cy \(\chi_{8619}(418, \cdot)\) n/a 7392 16
8619.2.da \(\chi_{8619}(146, \cdot)\) n/a 14464 16
8619.2.db \(\chi_{8619}(23, \cdot)\) n/a 14464 16
8619.2.de \(\chi_{8619}(64, \cdot)\) n/a 13056 24
8619.2.dg \(\chi_{8619}(47, \cdot)\) n/a 26112 24
8619.2.dh \(\chi_{8619}(203, \cdot)\) n/a 26112 24
8619.2.dk \(\chi_{8619}(86, \cdot)\) n/a 23328 24
8619.2.dl \(\chi_{8619}(200, \cdot)\) n/a 26112 24
8619.2.dn \(\chi_{8619}(157, \cdot)\) n/a 13152 24
8619.2.dq \(\chi_{8619}(322, \cdot)\) n/a 13056 24
8619.2.dr \(\chi_{8619}(205, \cdot)\) n/a 11664 24
8619.2.du \(\chi_{8619}(16, \cdot)\) n/a 13152 24
8619.2.dw \(\chi_{8619}(161, \cdot)\) n/a 52224 48
8619.2.dy \(\chi_{8619}(25, \cdot)\) n/a 26304 48
8619.2.dz \(\chi_{8619}(196, \cdot)\) n/a 26112 48
8619.2.ed \(\chi_{8619}(8, \cdot)\) n/a 52224 48
8619.2.ef \(\chi_{8619}(55, \cdot)\) n/a 26304 48
8619.2.eg \(\chi_{8619}(98, \cdot)\) n/a 52224 48
8619.2.ej \(\chi_{8619}(137, \cdot)\) n/a 46560 48
8619.2.ek \(\chi_{8619}(50, \cdot)\) n/a 52224 48
8619.2.en \(\chi_{8619}(149, \cdot)\) n/a 52224 48
8619.2.eo \(\chi_{8619}(4, \cdot)\) n/a 26112 48
8619.2.eq \(\chi_{8619}(73, \cdot)\) n/a 52416 96
8619.2.et \(\chi_{8619}(31, \cdot)\) n/a 52416 96
8619.2.ev \(\chi_{8619}(14, \cdot)\) n/a 104448 96
8619.2.ew \(\chi_{8619}(116, \cdot)\) n/a 104448 96
8619.2.ey \(\chi_{8619}(2, \cdot)\) n/a 104448 96
8619.2.fc \(\chi_{8619}(43, \cdot)\) n/a 52608 96
8619.2.fd \(\chi_{8619}(94, \cdot)\) n/a 52224 96
8619.2.ff \(\chi_{8619}(110, \cdot)\) n/a 104448 96
8619.2.fh \(\chi_{8619}(56, \cdot)\) n/a 208896 192
8619.2.fi \(\chi_{8619}(29, \cdot)\) n/a 208896 192
8619.2.fk \(\chi_{8619}(28, \cdot)\) n/a 104832 192
8619.2.fn \(\chi_{8619}(7, \cdot)\) n/a 104832 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8619))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8619)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(221))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(663))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2873))\)\(^{\oplus 2}\)