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Properties

Label 6035.2
Level 6035
Weight 2
Dimension 1314591
Nonzero newspaces 72
Sturm bound 5806080

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Defining parameters

Level: \( N \) = \( 6035 = 5 \cdot 17 \cdot 71 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(5806080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6035))\).

Total New Old
Modular forms 1460480 1327007 133473
Cusp forms 1442561 1314591 127970
Eisenstein series 17919 12416 5503

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6035))\)

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
6035.2.a \(\chi_{6035}(1, \cdot)\) 6035.2.a.a 36 1
6035.2.a.b 36
6035.2.a.c 44
6035.2.a.d 44
6035.2.a.e 49
6035.2.a.f 49
6035.2.a.g 58
6035.2.a.h 59
6035.2.b \(\chi_{6035}(4829, \cdot)\) n/a 560 1
6035.2.e \(\chi_{6035}(5184, \cdot)\) n/a 628 1
6035.2.f \(\chi_{6035}(356, \cdot)\) n/a 420 1
6035.2.j \(\chi_{6035}(2486, \cdot)\) n/a 840 2
6035.2.l \(\chi_{6035}(922, \cdot)\) n/a 1288 2
6035.2.n \(\chi_{6035}(2413, \cdot)\) n/a 1288 2
6035.2.o \(\chi_{6035}(2058, \cdot)\) n/a 1152 2
6035.2.q \(\chi_{6035}(2342, \cdot)\) n/a 1288 2
6035.2.s \(\chi_{6035}(1279, \cdot)\) n/a 1256 2
6035.2.u \(\chi_{6035}(341, \cdot)\) n/a 1536 4
6035.2.v \(\chi_{6035}(2806, \cdot)\) n/a 2304 6
6035.2.x \(\chi_{6035}(638, \cdot)\) n/a 2576 4
6035.2.z \(\chi_{6035}(1776, \cdot)\) n/a 1680 4
6035.2.ba \(\chi_{6035}(569, \cdot)\) n/a 2528 4
6035.2.bd \(\chi_{6035}(212, \cdot)\) n/a 2576 4
6035.2.bg \(\chi_{6035}(696, \cdot)\) n/a 1728 4
6035.2.bh \(\chi_{6035}(764, \cdot)\) n/a 2576 4
6035.2.bk \(\chi_{6035}(409, \cdot)\) n/a 2304 4
6035.2.bn \(\chi_{6035}(101, \cdot)\) n/a 2592 6
6035.2.bo \(\chi_{6035}(1954, \cdot)\) n/a 3864 6
6035.2.br \(\chi_{6035}(1599, \cdot)\) n/a 3456 6
6035.2.bt \(\chi_{6035}(498, \cdot)\) n/a 5040 8
6035.2.bu \(\chi_{6035}(354, \cdot)\) n/a 5152 8
6035.2.bx \(\chi_{6035}(141, \cdot)\) n/a 3456 8
6035.2.by \(\chi_{6035}(143, \cdot)\) n/a 5040 8
6035.2.cb \(\chi_{6035}(999, \cdot)\) n/a 5152 8
6035.2.cd \(\chi_{6035}(208, \cdot)\) n/a 5152 8
6035.2.cf \(\chi_{6035}(137, \cdot)\) n/a 4608 8
6035.2.cg \(\chi_{6035}(492, \cdot)\) n/a 5152 8
6035.2.ci \(\chi_{6035}(582, \cdot)\) n/a 5152 8
6035.2.ck \(\chi_{6035}(786, \cdot)\) n/a 3456 8
6035.2.cn \(\chi_{6035}(174, \cdot)\) n/a 7728 12
6035.2.cp \(\chi_{6035}(378, \cdot)\) n/a 7728 12
6035.2.cr \(\chi_{6035}(307, \cdot)\) n/a 6912 12
6035.2.cs \(\chi_{6035}(662, \cdot)\) n/a 7728 12
6035.2.cu \(\chi_{6035}(183, \cdot)\) n/a 7728 12
6035.2.cw \(\chi_{6035}(446, \cdot)\) n/a 5184 12
6035.2.cy \(\chi_{6035}(86, \cdot)\) n/a 9216 24
6035.2.cz \(\chi_{6035}(563, \cdot)\) n/a 10304 16
6035.2.dc \(\chi_{6035}(644, \cdot)\) n/a 10304 16
6035.2.dd \(\chi_{6035}(76, \cdot)\) n/a 6912 16
6035.2.df \(\chi_{6035}(117, \cdot)\) n/a 10304 16
6035.2.dh \(\chi_{6035}(168, \cdot)\) n/a 15456 24
6035.2.dk \(\chi_{6035}(179, \cdot)\) n/a 15456 24
6035.2.dl \(\chi_{6035}(321, \cdot)\) n/a 10368 24
6035.2.dn \(\chi_{6035}(893, \cdot)\) n/a 15456 24
6035.2.dp \(\chi_{6035}(154, \cdot)\) n/a 13824 24
6035.2.ds \(\chi_{6035}(169, \cdot)\) n/a 15456 24
6035.2.dt \(\chi_{6035}(16, \cdot)\) n/a 10368 24
6035.2.dx \(\chi_{6035}(167, \cdot)\) n/a 20608 32
6035.2.dy \(\chi_{6035}(46, \cdot)\) n/a 13824 32
6035.2.eb \(\chi_{6035}(14, \cdot)\) n/a 20608 32
6035.2.ec \(\chi_{6035}(57, \cdot)\) n/a 20608 32
6035.2.ef \(\chi_{6035}(37, \cdot)\) n/a 30912 48
6035.2.eg \(\chi_{6035}(41, \cdot)\) n/a 20736 48
6035.2.ej \(\chi_{6035}(39, \cdot)\) n/a 30912 48
6035.2.ek \(\chi_{6035}(48, \cdot)\) n/a 30912 48
6035.2.en \(\chi_{6035}(81, \cdot)\) n/a 20736 48
6035.2.ep \(\chi_{6035}(13, \cdot)\) n/a 30912 48
6035.2.er \(\chi_{6035}(33, \cdot)\) n/a 30912 48
6035.2.es \(\chi_{6035}(52, \cdot)\) n/a 27648 48
6035.2.eu \(\chi_{6035}(47, \cdot)\) n/a 30912 48
6035.2.ew \(\chi_{6035}(4, \cdot)\) n/a 30912 48
6035.2.ez \(\chi_{6035}(93, \cdot)\) n/a 61824 96
6035.2.fb \(\chi_{6035}(36, \cdot)\) n/a 41472 96
6035.2.fc \(\chi_{6035}(9, \cdot)\) n/a 61824 96
6035.2.ff \(\chi_{6035}(42, \cdot)\) n/a 61824 96
6035.2.fh \(\chi_{6035}(3, \cdot)\) n/a 123648 192
6035.2.fi \(\chi_{6035}(44, \cdot)\) n/a 123648 192
6035.2.fl \(\chi_{6035}(11, \cdot)\) n/a 82944 192
6035.2.fm \(\chi_{6035}(12, \cdot)\) n/a 123648 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6035))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6035)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(71))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(355))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1207))\)\(^{\oplus 2}\)