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Properties

Label 3660.1
Level 3660
Weight 1
Dimension 248
Nonzero newspaces 5
Newform subspaces 30
Sturm bound 714240
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3660 = 2^{2} \cdot 3 \cdot 5 \cdot 61 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 30 \)
Sturm bound: \(714240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3660))\).

Total New Old
Modular forms 5720 952 4768
Cusp forms 920 248 672
Eisenstein series 4800 704 4096

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 248 0 0 0

Trace form

\( 248 q + 8 q^{9} + O(q^{10}) \) \( 248 q + 8 q^{9} + 8 q^{25} + 8 q^{49} - 120 q^{70} + 8 q^{81} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3660))\)

We only show spaces with odd 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
3660.1.c \(\chi_{3660}(1709, \cdot)\) None 0 1
3660.1.e \(\chi_{3660}(1831, \cdot)\) None 0 1
3660.1.g \(\chi_{3660}(1219, \cdot)\) None 0 1
3660.1.i \(\chi_{3660}(2561, \cdot)\) None 0 1
3660.1.j \(\chi_{3660}(1099, \cdot)\) None 0 1
3660.1.l \(\chi_{3660}(2441, \cdot)\) None 0 1
3660.1.n \(\chi_{3660}(1829, \cdot)\) 3660.1.n.a 1 1
3660.1.n.b 1
3660.1.n.c 1
3660.1.n.d 1
3660.1.n.e 2
3660.1.n.f 2
3660.1.p \(\chi_{3660}(1951, \cdot)\) None 0 1
3660.1.r \(\chi_{3660}(1087, \cdot)\) None 0 2
3660.1.s \(\chi_{3660}(233, \cdot)\) None 0 2
3660.1.v \(\chi_{3660}(853, \cdot)\) None 0 2
3660.1.y \(\chi_{3660}(1463, \cdot)\) None 0 2
3660.1.z \(\chi_{3660}(2329, \cdot)\) None 0 2
3660.1.bc \(\chi_{3660}(599, \cdot)\) 3660.1.bc.a 2 2
3660.1.bc.b 2
3660.1.bc.c 2
3660.1.bc.d 2
3660.1.bc.e 4
3660.1.bc.f 4
3660.1.bd \(\chi_{3660}(721, \cdot)\) None 0 2
3660.1.bg \(\chi_{3660}(11, \cdot)\) None 0 2
3660.1.bi \(\chi_{3660}(733, \cdot)\) None 0 2
3660.1.bj \(\chi_{3660}(1343, \cdot)\) None 0 2
3660.1.bn \(\chi_{3660}(3283, \cdot)\) None 0 2
3660.1.bo \(\chi_{3660}(1697, \cdot)\) None 0 2
3660.1.br \(\chi_{3660}(1721, \cdot)\) None 0 2
3660.1.bt \(\chi_{3660}(379, \cdot)\) None 0 2
3660.1.bu \(\chi_{3660}(1051, \cdot)\) None 0 2
3660.1.bw \(\chi_{3660}(929, \cdot)\) None 0 2
3660.1.bx \(\chi_{3660}(1111, \cdot)\) None 0 2
3660.1.bz \(\chi_{3660}(989, \cdot)\) None 0 2
3660.1.cb \(\chi_{3660}(1661, \cdot)\) None 0 2
3660.1.cd \(\chi_{3660}(319, \cdot)\) None 0 2
3660.1.cg \(\chi_{3660}(619, \cdot)\) None 0 4
3660.1.ci \(\chi_{3660}(461, \cdot)\) None 0 4
3660.1.ck \(\chi_{3660}(149, \cdot)\) None 0 4
3660.1.cl \(\chi_{3660}(271, \cdot)\) None 0 4
3660.1.cm \(\chi_{3660}(569, \cdot)\) None 0 4
3660.1.co \(\chi_{3660}(691, \cdot)\) None 0 4
3660.1.cq \(\chi_{3660}(979, \cdot)\) None 0 4
3660.1.cs \(\chi_{3660}(41, \cdot)\) None 0 4
3660.1.cu \(\chi_{3660}(1493, \cdot)\) None 0 4
3660.1.cv \(\chi_{3660}(223, \cdot)\) None 0 4
3660.1.cy \(\chi_{3660}(563, \cdot)\) None 0 4
3660.1.db \(\chi_{3660}(1417, \cdot)\) None 0 4
3660.1.dd \(\chi_{3660}(1931, \cdot)\) None 0 4
3660.1.de \(\chi_{3660}(1321, \cdot)\) None 0 4
3660.1.dh \(\chi_{3660}(1199, \cdot)\) 3660.1.dh.a 4 4
3660.1.dh.b 4
3660.1.dh.c 4
3660.1.dh.d 4
3660.1.dh.e 8
3660.1.dh.f 8
3660.1.di \(\chi_{3660}(589, \cdot)\) None 0 4
3660.1.dl \(\chi_{3660}(47, \cdot)\) None 0 4
3660.1.dm \(\chi_{3660}(13, \cdot)\) None 0 4
3660.1.dq \(\chi_{3660}(833, \cdot)\) None 0 4
3660.1.dr \(\chi_{3660}(883, \cdot)\) None 0 4
3660.1.dt \(\chi_{3660}(953, \cdot)\) None 0 8
3660.1.du \(\chi_{3660}(643, \cdot)\) None 0 8
3660.1.dx \(\chi_{3660}(407, \cdot)\) None 0 8
3660.1.ea \(\chi_{3660}(613, \cdot)\) None 0 8
3660.1.eb \(\chi_{3660}(419, \cdot)\) 3660.1.eb.a 8 8
3660.1.eb.b 8
3660.1.eb.c 8
3660.1.eb.d 8
3660.1.eb.e 16
3660.1.eb.f 16
3660.1.ee \(\chi_{3660}(709, \cdot)\) None 0 8
3660.1.ef \(\chi_{3660}(191, \cdot)\) None 0 8
3660.1.ei \(\chi_{3660}(541, \cdot)\) None 0 8
3660.1.ek \(\chi_{3660}(203, \cdot)\) None 0 8
3660.1.el \(\chi_{3660}(217, \cdot)\) None 0 8
3660.1.ep \(\chi_{3660}(53, \cdot)\) None 0 8
3660.1.eq \(\chi_{3660}(343, \cdot)\) None 0 8
3660.1.es \(\chi_{3660}(391, \cdot)\) None 0 8
3660.1.eu \(\chi_{3660}(269, \cdot)\) None 0 8
3660.1.ew \(\chi_{3660}(161, \cdot)\) None 0 8
3660.1.ey \(\chi_{3660}(19, \cdot)\) None 0 8
3660.1.ez \(\chi_{3660}(1001, \cdot)\) None 0 8
3660.1.fb \(\chi_{3660}(199, \cdot)\) None 0 8
3660.1.fd \(\chi_{3660}(751, \cdot)\) None 0 8
3660.1.fe \(\chi_{3660}(629, \cdot)\) None 0 8
3660.1.fg \(\chi_{3660}(7, \cdot)\) None 0 16
3660.1.fh \(\chi_{3660}(17, \cdot)\) None 0 16
3660.1.fk \(\chi_{3660}(97, \cdot)\) None 0 16
3660.1.fn \(\chi_{3660}(107, \cdot)\) None 0 16
3660.1.fp \(\chi_{3660}(181, \cdot)\) None 0 16
3660.1.fq \(\chi_{3660}(71, \cdot)\) None 0 16
3660.1.ft \(\chi_{3660}(349, \cdot)\) None 0 16
3660.1.fu \(\chi_{3660}(59, \cdot)\) 3660.1.fu.a 16 16
3660.1.fu.b 16
3660.1.fu.c 16
3660.1.fu.d 16
3660.1.fu.e 32
3660.1.fu.f 32
3660.1.fx \(\chi_{3660}(73, \cdot)\) None 0 16
3660.1.fy \(\chi_{3660}(83, \cdot)\) None 0 16
3660.1.gc \(\chi_{3660}(67, \cdot)\) None 0 16
3660.1.gd \(\chi_{3660}(617, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3660))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3660)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(122))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(183))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(244))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(305))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(366))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(610))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(732))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(915))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1220))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1830))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3660))\)\(^{\oplus 1}\)