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Properties

Label 3648.1
Level 3648
Weight 1
Dimension 142
Nonzero newspaces 10
Newform subspaces 26
Sturm bound 737280
Trace bound 49

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Defining parameters

Level: \( N \) = \( 3648 = 2^{6} \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 26 \)
Sturm bound: \(737280\)
Trace bound: \(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3648))\).

Total New Old
Modular forms 5768 890 4878
Cusp forms 584 142 442
Eisenstein series 5184 748 4436

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 142 0 0 0

Trace form

\( 142 q + 10 q^{9} + O(q^{10}) \) \( 142 q + 10 q^{9} + 4 q^{13} + 4 q^{21} - 2 q^{25} + 4 q^{37} + 2 q^{49} - 6 q^{57} + 4 q^{61} + 24 q^{73} - 14 q^{81} + 4 q^{93} + 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3648))\)

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
3648.1.b \(\chi_{3648}(3647, \cdot)\) 3648.1.b.a 1 1
3648.1.b.b 1
3648.1.c \(\chi_{3648}(799, \cdot)\) None 0 1
3648.1.h \(\chi_{3648}(1217, \cdot)\) None 0 1
3648.1.i \(\chi_{3648}(1633, \cdot)\) None 0 1
3648.1.l \(\chi_{3648}(1823, \cdot)\) 3648.1.l.a 2 1
3648.1.l.b 2
3648.1.l.c 4
3648.1.l.d 4
3648.1.m \(\chi_{3648}(2623, \cdot)\) None 0 1
3648.1.n \(\chi_{3648}(3041, \cdot)\) None 0 1
3648.1.o \(\chi_{3648}(3457, \cdot)\) None 0 1
3648.1.s \(\chi_{3648}(305, \cdot)\) None 0 2
3648.1.t \(\chi_{3648}(721, \cdot)\) None 0 2
3648.1.w \(\chi_{3648}(911, \cdot)\) None 0 2
3648.1.x \(\chi_{3648}(1711, \cdot)\) None 0 2
3648.1.z \(\chi_{3648}(3199, \cdot)\) None 0 2
3648.1.ba \(\chi_{3648}(863, \cdot)\) 3648.1.ba.a 4 2
3648.1.ba.b 4
3648.1.be \(\chi_{3648}(2497, \cdot)\) None 0 2
3648.1.bf \(\chi_{3648}(353, \cdot)\) 3648.1.bf.a 4 2
3648.1.bf.b 4
3648.1.bf.c 4
3648.1.bf.d 4
3648.1.bi \(\chi_{3648}(1375, \cdot)\) None 0 2
3648.1.bj \(\chi_{3648}(2687, \cdot)\) 3648.1.bj.a 2 2
3648.1.bj.b 2
3648.1.bk \(\chi_{3648}(673, \cdot)\) None 0 2
3648.1.bl \(\chi_{3648}(1793, \cdot)\) 3648.1.bl.a 2 2
3648.1.bl.b 2
3648.1.bo \(\chi_{3648}(265, \cdot)\) None 0 4
3648.1.bp \(\chi_{3648}(343, \cdot)\) None 0 4
3648.1.bu \(\chi_{3648}(455, \cdot)\) None 0 4
3648.1.bv \(\chi_{3648}(761, \cdot)\) None 0 4
3648.1.bx \(\chi_{3648}(145, \cdot)\) None 0 4
3648.1.ca \(\chi_{3648}(881, \cdot)\) None 0 4
3648.1.cb \(\chi_{3648}(463, \cdot)\) None 0 4
3648.1.ce \(\chi_{3648}(335, \cdot)\) None 0 4
3648.1.cf \(\chi_{3648}(77, \cdot)\) None 0 8
3648.1.ci \(\chi_{3648}(227, \cdot)\) None 0 8
3648.1.ck \(\chi_{3648}(37, \cdot)\) None 0 8
3648.1.cl \(\chi_{3648}(115, \cdot)\) None 0 8
3648.1.cn \(\chi_{3648}(161, \cdot)\) 3648.1.cn.a 12 6
3648.1.cn.b 12
3648.1.cn.c 12
3648.1.cn.d 12
3648.1.co \(\chi_{3648}(193, \cdot)\) None 0 6
3648.1.cr \(\chi_{3648}(833, \cdot)\) 3648.1.cr.a 6 6
3648.1.cr.b 6
3648.1.ct \(\chi_{3648}(97, \cdot)\) None 0 6
3648.1.cu \(\chi_{3648}(383, \cdot)\) 3648.1.cu.a 6 6
3648.1.cu.b 6
3648.1.cw \(\chi_{3648}(415, \cdot)\) None 0 6
3648.1.cz \(\chi_{3648}(287, \cdot)\) 3648.1.cz.a 12 6
3648.1.cz.b 12
3648.1.db \(\chi_{3648}(511, \cdot)\) None 0 6
3648.1.de \(\chi_{3648}(425, \cdot)\) None 0 8
3648.1.df \(\chi_{3648}(407, \cdot)\) None 0 8
3648.1.dg \(\chi_{3648}(7, \cdot)\) None 0 8
3648.1.dh \(\chi_{3648}(217, \cdot)\) None 0 8
3648.1.dk \(\chi_{3648}(143, \cdot)\) None 0 12
3648.1.dm \(\chi_{3648}(175, \cdot)\) None 0 12
3648.1.dp \(\chi_{3648}(17, \cdot)\) None 0 12
3648.1.dr \(\chi_{3648}(241, \cdot)\) None 0 12
3648.1.dt \(\chi_{3648}(125, \cdot)\) None 0 16
3648.1.du \(\chi_{3648}(107, \cdot)\) None 0 16
3648.1.dw \(\chi_{3648}(373, \cdot)\) None 0 16
3648.1.dz \(\chi_{3648}(163, \cdot)\) None 0 16
3648.1.ea \(\chi_{3648}(71, \cdot)\) None 0 24
3648.1.ed \(\chi_{3648}(137, \cdot)\) None 0 24
3648.1.ef \(\chi_{3648}(55, \cdot)\) None 0 24
3648.1.eg \(\chi_{3648}(409, \cdot)\) None 0 24
3648.1.ej \(\chi_{3648}(43, \cdot)\) None 0 48
3648.1.el \(\chi_{3648}(13, \cdot)\) None 0 48
3648.1.em \(\chi_{3648}(59, \cdot)\) None 0 48
3648.1.eo \(\chi_{3648}(5, \cdot)\) None 0 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3648))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3648)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(912))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1824))\)\(^{\oplus 2}\)