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Properties

Label 4015.2
Level 4015
Weight 2
Dimension 572267
Nonzero newspaces 84
Sturm bound 2557440

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Defining parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(2557440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4015))\).

Total New Old
Modular forms 645120 579931 65189
Cusp forms 633601 572267 61334
Eisenstein series 11519 7664 3855

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4015))\)

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
4015.2.a \(\chi_{4015}(1, \cdot)\) 4015.2.a.a 1 1
4015.2.a.b 23
4015.2.a.c 23
4015.2.a.d 27
4015.2.a.e 27
4015.2.a.f 31
4015.2.a.g 32
4015.2.a.h 37
4015.2.a.i 38
4015.2.b \(\chi_{4015}(804, \cdot)\) n/a 360 1
4015.2.c \(\chi_{4015}(364, \cdot)\) n/a 368 1
4015.2.h \(\chi_{4015}(3576, \cdot)\) n/a 244 1
4015.2.i \(\chi_{4015}(1541, \cdot)\) n/a 488 2
4015.2.k \(\chi_{4015}(2509, \cdot)\) n/a 744 2
4015.2.m \(\chi_{4015}(1242, \cdot)\) n/a 864 2
4015.2.n \(\chi_{4015}(802, \cdot)\) n/a 880 2
4015.2.p \(\chi_{4015}(538, \cdot)\) n/a 880 2
4015.2.s \(\chi_{4015}(703, \cdot)\) n/a 880 2
4015.2.t \(\chi_{4015}(1706, \cdot)\) n/a 488 2
4015.2.v \(\chi_{4015}(366, \cdot)\) n/a 1152 4
4015.2.y \(\chi_{4015}(1761, \cdot)\) n/a 488 2
4015.2.z \(\chi_{4015}(2344, \cdot)\) n/a 736 2
4015.2.ba \(\chi_{4015}(2564, \cdot)\) n/a 736 2
4015.2.be \(\chi_{4015}(241, \cdot)\) n/a 1184 4
4015.2.bf \(\chi_{4015}(2168, \cdot)\) n/a 1480 4
4015.2.bh \(\chi_{4015}(562, \cdot)\) n/a 1480 4
4015.2.bj \(\chi_{4015}(1044, \cdot)\) n/a 1760 4
4015.2.bl \(\chi_{4015}(221, \cdot)\) n/a 1488 6
4015.2.bm \(\chi_{4015}(291, \cdot)\) n/a 1184 4
4015.2.br \(\chi_{4015}(729, \cdot)\) n/a 1760 4
4015.2.bs \(\chi_{4015}(1169, \cdot)\) n/a 1728 4
4015.2.bt \(\chi_{4015}(441, \cdot)\) n/a 976 4
4015.2.bv \(\chi_{4015}(1363, \cdot)\) n/a 1760 4
4015.2.by \(\chi_{4015}(362, \cdot)\) n/a 1760 4
4015.2.ca \(\chi_{4015}(593, \cdot)\) n/a 1760 4
4015.2.cb \(\chi_{4015}(373, \cdot)\) n/a 1760 4
4015.2.ce \(\chi_{4015}(1244, \cdot)\) n/a 1488 4
4015.2.cf \(\chi_{4015}(81, \cdot)\) n/a 2368 8
4015.2.ch \(\chi_{4015}(276, \cdot)\) n/a 1488 6
4015.2.ck \(\chi_{4015}(144, \cdot)\) n/a 2208 6
4015.2.cm \(\chi_{4015}(89, \cdot)\) n/a 2208 6
4015.2.co \(\chi_{4015}(246, \cdot)\) n/a 2368 8
4015.2.cp \(\chi_{4015}(338, \cdot)\) n/a 3520 8
4015.2.cs \(\chi_{4015}(173, \cdot)\) n/a 3520 8
4015.2.cu \(\chi_{4015}(72, \cdot)\) n/a 3520 8
4015.2.cv \(\chi_{4015}(293, \cdot)\) n/a 3456 8
4015.2.cx \(\chi_{4015}(119, \cdot)\) n/a 3520 8
4015.2.da \(\chi_{4015}(494, \cdot)\) n/a 3520 8
4015.2.dc \(\chi_{4015}(408, \cdot)\) n/a 2960 8
4015.2.de \(\chi_{4015}(518, \cdot)\) n/a 2960 8
4015.2.df \(\chi_{4015}(21, \cdot)\) n/a 2368 8
4015.2.dj \(\chi_{4015}(9, \cdot)\) n/a 3520 8
4015.2.dk \(\chi_{4015}(64, \cdot)\) n/a 3520 8
4015.2.dl \(\chi_{4015}(301, \cdot)\) n/a 2368 8
4015.2.dp \(\chi_{4015}(254, \cdot)\) n/a 4464 12
4015.2.dr \(\chi_{4015}(692, \cdot)\) n/a 5280 12
4015.2.ds \(\chi_{4015}(142, \cdot)\) n/a 5280 12
4015.2.du \(\chi_{4015}(32, \cdot)\) n/a 5280 12
4015.2.dx \(\chi_{4015}(98, \cdot)\) n/a 5280 12
4015.2.dy \(\chi_{4015}(111, \cdot)\) n/a 2976 12
4015.2.eb \(\chi_{4015}(314, \cdot)\) n/a 7040 16
4015.2.ed \(\chi_{4015}(752, \cdot)\) n/a 7040 16
4015.2.ef \(\chi_{4015}(168, \cdot)\) n/a 7040 16
4015.2.eg \(\chi_{4015}(51, \cdot)\) n/a 4736 16
4015.2.ei \(\chi_{4015}(16, \cdot)\) n/a 7104 24
4015.2.ej \(\chi_{4015}(49, \cdot)\) n/a 7040 16
4015.2.em \(\chi_{4015}(8, \cdot)\) n/a 7040 16
4015.2.en \(\chi_{4015}(138, \cdot)\) n/a 7040 16
4015.2.ep \(\chi_{4015}(733, \cdot)\) n/a 7040 16
4015.2.es \(\chi_{4015}(222, \cdot)\) n/a 7040 16
4015.2.eu \(\chi_{4015}(581, \cdot)\) n/a 4736 16
4015.2.ev \(\chi_{4015}(78, \cdot)\) n/a 8880 24
4015.2.ex \(\chi_{4015}(604, \cdot)\) n/a 10560 24
4015.2.ez \(\chi_{4015}(131, \cdot)\) n/a 7104 24
4015.2.fb \(\chi_{4015}(133, \cdot)\) n/a 8880 24
4015.2.fd \(\chi_{4015}(4, \cdot)\) n/a 10560 24
4015.2.ff \(\chi_{4015}(69, \cdot)\) n/a 10560 24
4015.2.fi \(\chi_{4015}(36, \cdot)\) n/a 7104 24
4015.2.fl \(\chi_{4015}(116, \cdot)\) n/a 9472 32
4015.2.fm \(\chi_{4015}(163, \cdot)\) n/a 14080 32
4015.2.fo \(\chi_{4015}(103, \cdot)\) n/a 14080 32
4015.2.fq \(\chi_{4015}(94, \cdot)\) n/a 14080 32
4015.2.ft \(\chi_{4015}(181, \cdot)\) n/a 14208 48
4015.2.fu \(\chi_{4015}(123, \cdot)\) n/a 21120 48
4015.2.fx \(\chi_{4015}(18, \cdot)\) n/a 21120 48
4015.2.fz \(\chi_{4015}(2, \cdot)\) n/a 21120 48
4015.2.ga \(\chi_{4015}(127, \cdot)\) n/a 21120 48
4015.2.gc \(\chi_{4015}(169, \cdot)\) n/a 21120 48
4015.2.gf \(\chi_{4015}(58, \cdot)\) n/a 42240 96
4015.2.gh \(\chi_{4015}(101, \cdot)\) n/a 28416 96
4015.2.gj \(\chi_{4015}(29, \cdot)\) n/a 42240 96
4015.2.gl \(\chi_{4015}(42, \cdot)\) n/a 42240 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4015))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4015)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(73))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(365))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(803))\)\(^{\oplus 2}\)