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Properties

Label 6615.2
Level 6615
Weight 2
Dimension 1054630
Nonzero newspaces 96
Sturm bound 6096384

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Defining parameters

Level: \( N \) = \( 6615 = 3^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(6096384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6615))\).

Total New Old
Modular forms 1538496 1063942 474554
Cusp forms 1509697 1054630 455067
Eisenstein series 28799 9312 19487

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6615))\)

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
6615.2.a \(\chi_{6615}(1, \cdot)\) 6615.2.a.a 1 1
6615.2.a.b 1
6615.2.a.c 1
6615.2.a.d 1
6615.2.a.e 1
6615.2.a.f 1
6615.2.a.g 1
6615.2.a.h 1
6615.2.a.i 1
6615.2.a.j 1
6615.2.a.k 2
6615.2.a.l 2
6615.2.a.m 2
6615.2.a.n 2
6615.2.a.o 2
6615.2.a.p 2
6615.2.a.q 2
6615.2.a.r 2
6615.2.a.s 2
6615.2.a.t 2
6615.2.a.u 2
6615.2.a.v 2
6615.2.a.w 2
6615.2.a.x 2
6615.2.a.y 3
6615.2.a.z 3
6615.2.a.ba 3
6615.2.a.bb 3
6615.2.a.bc 4
6615.2.a.bd 4
6615.2.a.be 4
6615.2.a.bf 4
6615.2.a.bg 4
6615.2.a.bh 4
6615.2.a.bi 4
6615.2.a.bj 4
6615.2.a.bk 5
6615.2.a.bl 5
6615.2.a.bm 5
6615.2.a.bn 5
6615.2.a.bo 5
6615.2.a.bp 5
6615.2.a.bq 5
6615.2.a.br 5
6615.2.a.bs 6
6615.2.a.bt 6
6615.2.a.bu 7
6615.2.a.bv 7
6615.2.a.bw 7
6615.2.a.bx 7
6615.2.a.by 8
6615.2.a.bz 8
6615.2.a.ca 8
6615.2.a.cb 8
6615.2.a.cc 12
6615.2.a.cd 12
6615.2.b \(\chi_{6615}(5291, \cdot)\) n/a 212 1
6615.2.d \(\chi_{6615}(1324, \cdot)\) n/a 328 1
6615.2.g \(\chi_{6615}(6614, \cdot)\) n/a 320 1
6615.2.i \(\chi_{6615}(2206, \cdot)\) n/a 328 2
6615.2.j \(\chi_{6615}(2431, \cdot)\) n/a 428 2
6615.2.k \(\chi_{6615}(361, \cdot)\) n/a 320 2
6615.2.l \(\chi_{6615}(226, \cdot)\) n/a 320 2
6615.2.m \(\chi_{6615}(2402, \cdot)\) n/a 656 2
6615.2.p \(\chi_{6615}(1567, \cdot)\) n/a 640 2
6615.2.r \(\chi_{6615}(1549, \cdot)\) n/a 464 2
6615.2.t \(\chi_{6615}(521, \cdot)\) n/a 320 2
6615.2.u \(\chi_{6615}(1979, \cdot)\) n/a 464 2
6615.2.z \(\chi_{6615}(2204, \cdot)\) n/a 464 2
6615.2.bb \(\chi_{6615}(4049, \cdot)\) n/a 640 2
6615.2.be \(\chi_{6615}(656, \cdot)\) n/a 320 2
6615.2.bf \(\chi_{6615}(3754, \cdot)\) n/a 640 2
6615.2.bh \(\chi_{6615}(3529, \cdot)\) n/a 472 2
6615.2.bj \(\chi_{6615}(2726, \cdot)\) n/a 428 2
6615.2.bl \(\chi_{6615}(881, \cdot)\) n/a 320 2
6615.2.bo \(\chi_{6615}(1684, \cdot)\) n/a 464 2
6615.2.bq \(\chi_{6615}(1844, \cdot)\) n/a 464 2
6615.2.bs \(\chi_{6615}(946, \cdot)\) n/a 1800 6
6615.2.bt \(\chi_{6615}(961, \cdot)\) n/a 2880 6
6615.2.bu \(\chi_{6615}(736, \cdot)\) n/a 2952 6
6615.2.bv \(\chi_{6615}(1096, \cdot)\) n/a 2880 6
6615.2.bw \(\chi_{6615}(1207, \cdot)\) n/a 928 4
6615.2.bz \(\chi_{6615}(422, \cdot)\) n/a 928 4
6615.2.cb \(\chi_{6615}(557, \cdot)\) n/a 928 4
6615.2.cd \(\chi_{6615}(1648, \cdot)\) n/a 1280 4
6615.2.cf \(\chi_{6615}(2008, \cdot)\) n/a 928 4
6615.2.cg \(\chi_{6615}(197, \cdot)\) n/a 944 4
6615.2.ci \(\chi_{6615}(863, \cdot)\) n/a 1280 4
6615.2.ck \(\chi_{6615}(1342, \cdot)\) n/a 928 4
6615.2.cn \(\chi_{6615}(944, \cdot)\) n/a 2688 6
6615.2.cq \(\chi_{6615}(379, \cdot)\) n/a 2688 6
6615.2.cs \(\chi_{6615}(566, \cdot)\) n/a 1800 6
6615.2.ct \(\chi_{6615}(509, \cdot)\) n/a 4272 6
6615.2.cy \(\chi_{6615}(374, \cdot)\) n/a 4272 6
6615.2.da \(\chi_{6615}(734, \cdot)\) n/a 4272 6
6615.2.dc \(\chi_{6615}(214, \cdot)\) n/a 4272 6
6615.2.df \(\chi_{6615}(1256, \cdot)\) n/a 2880 6
6615.2.dh \(\chi_{6615}(146, \cdot)\) n/a 2880 6
6615.2.dj \(\chi_{6615}(79, \cdot)\) n/a 4272 6
6615.2.dl \(\chi_{6615}(589, \cdot)\) n/a 4368 6
6615.2.dm \(\chi_{6615}(1391, \cdot)\) n/a 2880 6
6615.2.do \(\chi_{6615}(46, \cdot)\) n/a 2688 12
6615.2.dp \(\chi_{6615}(856, \cdot)\) n/a 2688 12
6615.2.dq \(\chi_{6615}(541, \cdot)\) n/a 3576 12
6615.2.dr \(\chi_{6615}(316, \cdot)\) n/a 2688 12
6615.2.dt \(\chi_{6615}(433, \cdot)\) n/a 5376 12
6615.2.du \(\chi_{6615}(323, \cdot)\) n/a 5376 12
6615.2.dx \(\chi_{6615}(263, \cdot)\) n/a 8544 12
6615.2.dy \(\chi_{6615}(97, \cdot)\) n/a 8544 12
6615.2.ea \(\chi_{6615}(313, \cdot)\) n/a 8544 12
6615.2.ec \(\chi_{6615}(932, \cdot)\) n/a 8736 12
6615.2.ee \(\chi_{6615}(128, \cdot)\) n/a 8544 12
6615.2.eh \(\chi_{6615}(178, \cdot)\) n/a 8544 12
6615.2.ej \(\chi_{6615}(719, \cdot)\) n/a 3984 12
6615.2.el \(\chi_{6615}(289, \cdot)\) n/a 3984 12
6615.2.eo \(\chi_{6615}(251, \cdot)\) n/a 2688 12
6615.2.eq \(\chi_{6615}(26, \cdot)\) n/a 3576 12
6615.2.es \(\chi_{6615}(64, \cdot)\) n/a 3984 12
6615.2.eu \(\chi_{6615}(109, \cdot)\) n/a 5376 12
6615.2.ev \(\chi_{6615}(206, \cdot)\) n/a 2688 12
6615.2.ey \(\chi_{6615}(269, \cdot)\) n/a 5376 12
6615.2.fa \(\chi_{6615}(314, \cdot)\) n/a 3984 12
6615.2.ff \(\chi_{6615}(89, \cdot)\) n/a 3984 12
6615.2.fg \(\chi_{6615}(341, \cdot)\) n/a 2688 12
6615.2.fi \(\chi_{6615}(424, \cdot)\) n/a 3984 12
6615.2.fk \(\chi_{6615}(121, \cdot)\) n/a 24192 36
6615.2.fl \(\chi_{6615}(106, \cdot)\) n/a 24192 36
6615.2.fm \(\chi_{6615}(16, \cdot)\) n/a 24192 36
6615.2.fn \(\chi_{6615}(208, \cdot)\) n/a 7968 24
6615.2.fp \(\chi_{6615}(8, \cdot)\) n/a 7968 24
6615.2.fr \(\chi_{6615}(53, \cdot)\) n/a 10752 24
6615.2.fu \(\chi_{6615}(82, \cdot)\) n/a 10752 24
6615.2.fw \(\chi_{6615}(118, \cdot)\) n/a 7968 24
6615.2.fy \(\chi_{6615}(368, \cdot)\) n/a 7968 24
6615.2.ga \(\chi_{6615}(233, \cdot)\) n/a 7968 24
6615.2.gb \(\chi_{6615}(73, \cdot)\) n/a 7968 24
6615.2.ge \(\chi_{6615}(101, \cdot)\) n/a 24192 36
6615.2.gf \(\chi_{6615}(169, \cdot)\) n/a 36144 36
6615.2.gh \(\chi_{6615}(4, \cdot)\) n/a 36144 36
6615.2.gj \(\chi_{6615}(41, \cdot)\) n/a 24192 36
6615.2.gl \(\chi_{6615}(236, \cdot)\) n/a 24192 36
6615.2.go \(\chi_{6615}(184, \cdot)\) n/a 36144 36
6615.2.gq \(\chi_{6615}(104, \cdot)\) n/a 36144 36
6615.2.gs \(\chi_{6615}(59, \cdot)\) n/a 36144 36
6615.2.gx \(\chi_{6615}(164, \cdot)\) n/a 36144 36
6615.2.gy \(\chi_{6615}(23, \cdot)\) n/a 72288 72
6615.2.hb \(\chi_{6615}(157, \cdot)\) n/a 72288 72
6615.2.hd \(\chi_{6615}(13, \cdot)\) n/a 72288 72
6615.2.hf \(\chi_{6615}(2, \cdot)\) n/a 72288 72
6615.2.hh \(\chi_{6615}(92, \cdot)\) n/a 72288 72
6615.2.hi \(\chi_{6615}(52, \cdot)\) n/a 72288 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6615))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6615)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(945))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1323))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2205))\)\(^{\oplus 2}\)