Properties

Label 6031.2
Level 6031
Weight 2
Dimension 1506411
Nonzero newspaces 105
Sturm bound 6057504

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Defining parameters

Level: \( N \) = \( 6031 = 37 \cdot 163 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 105 \)
Sturm bound: \(6057504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6031))\).

Total New Old
Modular forms 1520208 1517683 2525
Cusp forms 1508545 1506411 2134
Eisenstein series 11663 11272 391

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6031))\)

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
6031.2.a \(\chi_{6031}(1, \cdot)\) 6031.2.a.a 1 1
6031.2.a.b 109
6031.2.a.c 110
6031.2.a.d 133
6031.2.a.e 134
6031.2.c \(\chi_{6031}(4402, \cdot)\) n/a 512 1
6031.2.e \(\chi_{6031}(1305, \cdot)\) n/a 1028 2
6031.2.f \(\chi_{6031}(2875, \cdot)\) n/a 1032 2
6031.2.g \(\chi_{6031}(593, \cdot)\) n/a 984 2
6031.2.h \(\chi_{6031}(1897, \cdot)\) n/a 1032 2
6031.2.j \(\chi_{6031}(1955, \cdot)\) n/a 1032 2
6031.2.l \(\chi_{6031}(3690, \cdot)\) n/a 1032 2
6031.2.p \(\chi_{6031}(221, \cdot)\) n/a 1032 2
6031.2.q \(\chi_{6031}(2120, \cdot)\) n/a 1024 2
6031.2.r \(\chi_{6031}(2712, \cdot)\) n/a 1032 2
6031.2.w \(\chi_{6031}(366, \cdot)\) n/a 3108 6
6031.2.x \(\chi_{6031}(1181, \cdot)\) n/a 3108 6
6031.2.y \(\chi_{6031}(248, \cdot)\) n/a 3096 6
6031.2.z \(\chi_{6031}(38, \cdot)\) n/a 2952 6
6031.2.ba \(\chi_{6031}(2972, \cdot)\) n/a 3108 6
6031.2.bb \(\chi_{6031}(201, \cdot)\) n/a 3108 6
6031.2.bc \(\chi_{6031}(303, \cdot)\) n/a 3108 6
6031.2.bd \(\chi_{6031}(164, \cdot)\) n/a 3084 6
6031.2.be \(\chi_{6031}(2014, \cdot)\) n/a 3108 6
6031.2.bf \(\chi_{6031}(710, \cdot)\) n/a 3108 6
6031.2.bg \(\chi_{6031}(1342, \cdot)\) n/a 3096 6
6031.2.bh \(\chi_{6031}(53, \cdot)\) n/a 3108 6
6031.2.bj \(\chi_{6031}(711, \cdot)\) n/a 2064 4
6031.2.bk \(\chi_{6031}(105, \cdot)\) n/a 2064 4
6031.2.bl \(\chi_{6031}(162, \cdot)\) n/a 2064 4
6031.2.bp \(\chi_{6031}(874, \cdot)\) n/a 2064 4
6031.2.bq \(\chi_{6031}(411, \cdot)\) n/a 3108 6
6031.2.bv \(\chi_{6031}(1063, \cdot)\) n/a 3096 6
6031.2.cb \(\chi_{6031}(58, \cdot)\) n/a 3108 6
6031.2.cc \(\chi_{6031}(1468, \cdot)\) n/a 3072 6
6031.2.cd \(\chi_{6031}(1362, \cdot)\) n/a 3108 6
6031.2.ci \(\chi_{6031}(622, \cdot)\) n/a 3108 6
6031.2.cj \(\chi_{6031}(1505, \cdot)\) n/a 3108 6
6031.2.cm \(\chi_{6031}(955, \cdot)\) n/a 3108 6
6031.2.cs \(\chi_{6031}(85, \cdot)\) n/a 3096 6
6031.2.ct \(\chi_{6031}(2367, \cdot)\) n/a 3096 6
6031.2.cw \(\chi_{6031}(855, \cdot)\) n/a 3108 6
6031.2.cy \(\chi_{6031}(40, \cdot)\) n/a 3108 6
6031.2.da \(\chi_{6031}(810, \cdot)\) n/a 9324 18
6031.2.db \(\chi_{6031}(441, \cdot)\) n/a 9324 18
6031.2.dc \(\chi_{6031}(778, \cdot)\) n/a 8856 18
6031.2.dd \(\chi_{6031}(158, \cdot)\) n/a 9288 18
6031.2.de \(\chi_{6031}(787, \cdot)\) n/a 9288 18
6031.2.df \(\chi_{6031}(514, \cdot)\) n/a 9324 18
6031.2.dg \(\chi_{6031}(155, \cdot)\) n/a 9324 18
6031.2.dh \(\chi_{6031}(604, \cdot)\) n/a 9324 18
6031.2.di \(\chi_{6031}(1163, \cdot)\) n/a 9324 18
6031.2.dk \(\chi_{6031}(449, \cdot)\) n/a 6216 12
6031.2.dl \(\chi_{6031}(241, \cdot)\) n/a 6216 12
6031.2.dm \(\chi_{6031}(775, \cdot)\) n/a 6216 12
6031.2.dp \(\chi_{6031}(651, \cdot)\) n/a 6216 12
6031.2.dq \(\chi_{6031}(594, \cdot)\) n/a 6216 12
6031.2.dt \(\chi_{6031}(125, \cdot)\) n/a 6192 12
6031.2.dv \(\chi_{6031}(23, \cdot)\) n/a 6192 12
6031.2.dw \(\chi_{6031}(512, \cdot)\) n/a 6192 12
6031.2.ea \(\chi_{6031}(59, \cdot)\) n/a 6216 12
6031.2.eb \(\chi_{6031}(838, \cdot)\) n/a 6216 12
6031.2.ec \(\chi_{6031}(612, \cdot)\) n/a 6216 12
6031.2.eg \(\chi_{6031}(893, \cdot)\) n/a 6216 12
6031.2.ei \(\chi_{6031}(115, \cdot)\) n/a 9324 18
6031.2.em \(\chi_{6031}(136, \cdot)\) n/a 9324 18
6031.2.en \(\chi_{6031}(77, \cdot)\) n/a 9324 18
6031.2.ep \(\chi_{6031}(132, \cdot)\) n/a 9324 18
6031.2.ev \(\chi_{6031}(36, \cdot)\) n/a 9288 18
6031.2.ew \(\chi_{6031}(64, \cdot)\) n/a 9288 18
6031.2.ez \(\chi_{6031}(788, \cdot)\) n/a 9288 18
6031.2.fd \(\chi_{6031}(21, \cdot)\) n/a 9324 18
6031.2.fg \(\chi_{6031}(65, \cdot)\) n/a 9324 18
6031.2.fi \(\chi_{6031}(416, \cdot)\) n/a 27918 54
6031.2.fj \(\chi_{6031}(33, \cdot)\) n/a 27918 54
6031.2.fk \(\chi_{6031}(46, \cdot)\) n/a 27918 54
6031.2.fl \(\chi_{6031}(16, \cdot)\) n/a 27918 54
6031.2.fm \(\chi_{6031}(223, \cdot)\) n/a 26568 54
6031.2.fn \(\chi_{6031}(10, \cdot)\) n/a 27972 54
6031.2.fo \(\chi_{6031}(26, \cdot)\) n/a 27972 54
6031.2.fp \(\chi_{6031}(9, \cdot)\) n/a 27918 54
6031.2.fq \(\chi_{6031}(34, \cdot)\) n/a 27918 54
6031.2.fs \(\chi_{6031}(13, \cdot)\) n/a 18648 36
6031.2.fu \(\chi_{6031}(8, \cdot)\) n/a 18576 36
6031.2.fv \(\chi_{6031}(31, \cdot)\) n/a 18576 36
6031.2.fw \(\chi_{6031}(320, \cdot)\) n/a 18648 36
6031.2.fz \(\chi_{6031}(200, \cdot)\) n/a 18648 36
6031.2.gb \(\chi_{6031}(98, \cdot)\) n/a 18648 36
6031.2.ge \(\chi_{6031}(171, \cdot)\) n/a 18576 36
6031.2.gf \(\chi_{6031}(357, \cdot)\) n/a 18648 36
6031.2.gg \(\chi_{6031}(5, \cdot)\) n/a 18648 36
6031.2.gl \(\chi_{6031}(41, \cdot)\) n/a 27918 54
6031.2.gm \(\chi_{6031}(225, \cdot)\) n/a 27918 54
6031.2.gn \(\chi_{6031}(250, \cdot)\) n/a 27918 54
6031.2.gs \(\chi_{6031}(4, \cdot)\) n/a 27918 54
6031.2.gu \(\chi_{6031}(307, \cdot)\) n/a 27972 54
6031.2.gx \(\chi_{6031}(258, \cdot)\) n/a 27972 54
6031.2.hb \(\chi_{6031}(196, \cdot)\) n/a 27972 54
6031.2.hc \(\chi_{6031}(62, \cdot)\) n/a 27918 54
6031.2.hj \(\chi_{6031}(151, \cdot)\) n/a 27918 54
6031.2.hl \(\chi_{6031}(50, \cdot)\) n/a 55836 108
6031.2.hm \(\chi_{6031}(42, \cdot)\) n/a 55836 108
6031.2.hn \(\chi_{6031}(72, \cdot)\) n/a 55836 108
6031.2.hp \(\chi_{6031}(45, \cdot)\) n/a 55944 108
6031.2.hs \(\chi_{6031}(29, \cdot)\) n/a 55944 108
6031.2.hu \(\chi_{6031}(68, \cdot)\) n/a 55944 108
6031.2.hv \(\chi_{6031}(18, \cdot)\) n/a 55836 108
6031.2.hy \(\chi_{6031}(2, \cdot)\) n/a 55836 108
6031.2.ib \(\chi_{6031}(20, \cdot)\) n/a 55836 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6031))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6031)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(163))\)\(^{\oplus 2}\)