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Properties

Label 2160.1
Level 2160
Weight 1
Dimension 54
Nonzero newspaces 7
Newform subspaces 11
Sturm bound 248832
Trace bound 10

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Defining parameters

Level: \( N \) = \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 11 \)
Sturm bound: \(248832\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2160))\).

Total New Old
Modular forms 3758 486 3272
Cusp forms 398 54 344
Eisenstein series 3360 432 2928

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 34 0 20 0

Trace form

\( 54 q - 8 q^{4} - 2 q^{5} + O(q^{10}) \) \( 54 q - 8 q^{4} - 2 q^{5} + 4 q^{10} + 4 q^{13} + 8 q^{16} + 6 q^{19} + 4 q^{22} - 8 q^{29} + 10 q^{31} + 8 q^{34} - 4 q^{40} - 10 q^{41} + 4 q^{43} - 6 q^{45} - 8 q^{46} + 12 q^{49} + 4 q^{52} + 4 q^{55} - 4 q^{58} - 10 q^{61} - 8 q^{64} - 8 q^{67} - 12 q^{69} - 8 q^{70} - 8 q^{76} + 6 q^{79} - 8 q^{82} + 2 q^{85} - 4 q^{88} + 4 q^{89} - 4 q^{91} - 8 q^{94} + 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2160))\)

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
2160.1.c \(\chi_{2160}(1889, \cdot)\) 2160.1.c.a 1 1
2160.1.c.b 1
2160.1.c.c 4
2160.1.e \(\chi_{2160}(271, \cdot)\) None 0 1
2160.1.g \(\chi_{2160}(1351, \cdot)\) None 0 1
2160.1.i \(\chi_{2160}(809, \cdot)\) None 0 1
2160.1.j \(\chi_{2160}(1999, \cdot)\) None 0 1
2160.1.l \(\chi_{2160}(161, \cdot)\) None 0 1
2160.1.n \(\chi_{2160}(1241, \cdot)\) None 0 1
2160.1.p \(\chi_{2160}(919, \cdot)\) None 0 1
2160.1.r \(\chi_{2160}(379, \cdot)\) 2160.1.r.a 8 2
2160.1.s \(\chi_{2160}(701, \cdot)\) None 0 2
2160.1.v \(\chi_{2160}(647, \cdot)\) None 0 2
2160.1.y \(\chi_{2160}(217, \cdot)\) None 0 2
2160.1.ba \(\chi_{2160}(107, \cdot)\) 2160.1.ba.a 4 2
2160.1.bb \(\chi_{2160}(757, \cdot)\) None 0 2
2160.1.be \(\chi_{2160}(1187, \cdot)\) 2160.1.be.a 4 2
2160.1.bf \(\chi_{2160}(1837, \cdot)\) None 0 2
2160.1.bh \(\chi_{2160}(433, \cdot)\) None 0 2
2160.1.bk \(\chi_{2160}(863, \cdot)\) None 0 2
2160.1.bn \(\chi_{2160}(269, \cdot)\) 2160.1.bn.a 4 2
2160.1.bn.b 4
2160.1.bn.c 8
2160.1.bo \(\chi_{2160}(811, \cdot)\) None 0 2
2160.1.bp \(\chi_{2160}(199, \cdot)\) None 0 2
2160.1.bq \(\chi_{2160}(521, \cdot)\) None 0 2
2160.1.bs \(\chi_{2160}(881, \cdot)\) None 0 2
2160.1.bu \(\chi_{2160}(559, \cdot)\) 2160.1.bu.a 4 2
2160.1.bx \(\chi_{2160}(89, \cdot)\) None 0 2
2160.1.bz \(\chi_{2160}(631, \cdot)\) None 0 2
2160.1.cb \(\chi_{2160}(991, \cdot)\) None 0 2
2160.1.cd \(\chi_{2160}(449, \cdot)\) None 0 2
2160.1.ch \(\chi_{2160}(91, \cdot)\) None 0 4
2160.1.ci \(\chi_{2160}(629, \cdot)\) None 0 4
2160.1.ck \(\chi_{2160}(577, \cdot)\) None 0 4
2160.1.cl \(\chi_{2160}(143, \cdot)\) None 0 4
2160.1.co \(\chi_{2160}(397, \cdot)\) None 0 4
2160.1.cp \(\chi_{2160}(467, \cdot)\) None 0 4
2160.1.cs \(\chi_{2160}(37, \cdot)\) None 0 4
2160.1.ct \(\chi_{2160}(827, \cdot)\) None 0 4
2160.1.cw \(\chi_{2160}(503, \cdot)\) None 0 4
2160.1.cx \(\chi_{2160}(73, \cdot)\) None 0 4
2160.1.cz \(\chi_{2160}(341, \cdot)\) None 0 4
2160.1.da \(\chi_{2160}(19, \cdot)\) None 0 4
2160.1.de \(\chi_{2160}(151, \cdot)\) None 0 6
2160.1.df \(\chi_{2160}(209, \cdot)\) None 0 6
2160.1.dg \(\chi_{2160}(329, \cdot)\) None 0 6
2160.1.dh \(\chi_{2160}(31, \cdot)\) None 0 6
2160.1.dk \(\chi_{2160}(401, \cdot)\) None 0 6
2160.1.dl \(\chi_{2160}(439, \cdot)\) None 0 6
2160.1.dq \(\chi_{2160}(79, \cdot)\) 2160.1.dq.a 12 6
2160.1.dr \(\chi_{2160}(41, \cdot)\) None 0 6
2160.1.ds \(\chi_{2160}(29, \cdot)\) None 0 12
2160.1.dt \(\chi_{2160}(211, \cdot)\) None 0 12
2160.1.dw \(\chi_{2160}(47, \cdot)\) None 0 12
2160.1.dx \(\chi_{2160}(313, \cdot)\) None 0 12
2160.1.eb \(\chi_{2160}(133, \cdot)\) None 0 12
2160.1.ed \(\chi_{2160}(203, \cdot)\) None 0 12
2160.1.ef \(\chi_{2160}(83, \cdot)\) None 0 12
2160.1.eh \(\chi_{2160}(13, \cdot)\) None 0 12
2160.1.ei \(\chi_{2160}(23, \cdot)\) None 0 12
2160.1.ej \(\chi_{2160}(97, \cdot)\) None 0 12
2160.1.em \(\chi_{2160}(139, \cdot)\) None 0 12
2160.1.en \(\chi_{2160}(101, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2160))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2160)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1080))\)\(^{\oplus 2}\)