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Properties

Label 2448.1
Level 2448
Weight 1
Dimension 60
Nonzero newspaces 9
Newform subspaces 15
Sturm bound 331776
Trace bound 25

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Defining parameters

Level: \( N \) = \( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 15 \)
Sturm bound: \(331776\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2448))\).

Total New Old
Modular forms 4128 668 3460
Cusp forms 544 60 484
Eisenstein series 3584 608 2976

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 44 0 16 0

Trace form

\( 60 q - 4 q^{4} + O(q^{10}) \) \( 60 q - 4 q^{4} - 8 q^{13} + 4 q^{16} - 6 q^{17} + 8 q^{19} - 8 q^{21} + 4 q^{25} + 8 q^{29} + 4 q^{31} + 12 q^{33} - 4 q^{37} + 4 q^{41} - 8 q^{43} - 8 q^{49} + 4 q^{52} + 8 q^{53} - 4 q^{57} - 8 q^{61} - 4 q^{64} - 4 q^{65} + 4 q^{67} + 12 q^{69} - 4 q^{73} - 4 q^{76} + 4 q^{79} + 8 q^{81} + 8 q^{89} - 4 q^{93} - 8 q^{94} + 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2448))\)

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
2448.1.b \(\chi_{2448}(1529, \cdot)\) None 0 1
2448.1.d \(\chi_{2448}(919, \cdot)\) None 0 1
2448.1.g \(\chi_{2448}(2177, \cdot)\) None 0 1
2448.1.i \(\chi_{2448}(271, \cdot)\) 2448.1.i.a 2 1
2448.1.i.b 2
2448.1.i.c 4
2448.1.k \(\chi_{2448}(2143, \cdot)\) None 0 1
2448.1.m \(\chi_{2448}(305, \cdot)\) 2448.1.m.a 2 1
2448.1.m.b 2
2448.1.n \(\chi_{2448}(1495, \cdot)\) None 0 1
2448.1.p \(\chi_{2448}(953, \cdot)\) None 0 1
2448.1.r \(\chi_{2448}(523, \cdot)\) None 0 2
2448.1.u \(\chi_{2448}(557, \cdot)\) None 0 2
2448.1.w \(\chi_{2448}(883, \cdot)\) 2448.1.w.a 2 2
2448.1.w.b 2
2448.1.y \(\chi_{2448}(341, \cdot)\) None 0 2
2448.1.ba \(\chi_{2448}(55, \cdot)\) None 0 2
2448.1.bc \(\chi_{2448}(89, \cdot)\) None 0 2
2448.1.bd \(\chi_{2448}(1169, \cdot)\) 2448.1.bd.a 4 2
2448.1.bf \(\chi_{2448}(1135, \cdot)\) 2448.1.bf.a 2 2
2448.1.bf.b 2
2448.1.bh \(\chi_{2448}(917, \cdot)\) None 0 2
2448.1.bj \(\chi_{2448}(307, \cdot)\) None 0 2
2448.1.bl \(\chi_{2448}(701, \cdot)\) None 0 2
2448.1.bo \(\chi_{2448}(667, \cdot)\) None 0 2
2448.1.bp \(\chi_{2448}(137, \cdot)\) None 0 2
2448.1.br \(\chi_{2448}(679, \cdot)\) None 0 2
2448.1.bs \(\chi_{2448}(1121, \cdot)\) None 0 2
2448.1.bu \(\chi_{2448}(511, \cdot)\) None 0 2
2448.1.bw \(\chi_{2448}(1087, \cdot)\) 2448.1.bw.a 8 2
2448.1.by \(\chi_{2448}(545, \cdot)\) None 0 2
2448.1.cb \(\chi_{2448}(103, \cdot)\) None 0 2
2448.1.cd \(\chi_{2448}(713, \cdot)\) None 0 2
2448.1.ce \(\chi_{2448}(161, \cdot)\) None 0 4
2448.1.cf \(\chi_{2448}(127, \cdot)\) 2448.1.cf.a 4 4
2448.1.ck \(\chi_{2448}(451, \cdot)\) None 0 4
2448.1.cl \(\chi_{2448}(485, \cdot)\) None 0 4
2448.1.co \(\chi_{2448}(19, \cdot)\) None 0 4
2448.1.cp \(\chi_{2448}(53, \cdot)\) None 0 4
2448.1.cs \(\chi_{2448}(665, \cdot)\) None 0 4
2448.1.ct \(\chi_{2448}(631, \cdot)\) None 0 4
2448.1.cv \(\chi_{2448}(115, \cdot)\) None 0 4
2448.1.cw \(\chi_{2448}(149, \cdot)\) None 0 4
2448.1.cz \(\chi_{2448}(715, \cdot)\) None 0 4
2448.1.db \(\chi_{2448}(101, \cdot)\) None 0 4
2448.1.dc \(\chi_{2448}(353, \cdot)\) None 0 4
2448.1.de \(\chi_{2448}(319, \cdot)\) 2448.1.de.a 8 4
2448.1.dh \(\chi_{2448}(727, \cdot)\) None 0 4
2448.1.dj \(\chi_{2448}(761, \cdot)\) None 0 4
2448.1.dk \(\chi_{2448}(749, \cdot)\) None 0 4
2448.1.dm \(\chi_{2448}(67, \cdot)\) None 0 4
2448.1.dp \(\chi_{2448}(293, \cdot)\) None 0 4
2448.1.dq \(\chi_{2448}(259, \cdot)\) None 0 4
2448.1.ds \(\chi_{2448}(181, \cdot)\) None 0 8
2448.1.dv \(\chi_{2448}(827, \cdot)\) None 0 8
2448.1.dw \(\chi_{2448}(71, \cdot)\) None 0 8
2448.1.dz \(\chi_{2448}(73, \cdot)\) None 0 8
2448.1.ea \(\chi_{2448}(721, \cdot)\) None 0 8
2448.1.ed \(\chi_{2448}(143, \cdot)\) 2448.1.ed.a 8 8
2448.1.ed.b 8
2448.1.ee \(\chi_{2448}(37, \cdot)\) None 0 8
2448.1.eh \(\chi_{2448}(107, \cdot)\) None 0 8
2448.1.ek \(\chi_{2448}(185, \cdot)\) None 0 8
2448.1.el \(\chi_{2448}(151, \cdot)\) None 0 8
2448.1.em \(\chi_{2448}(427, \cdot)\) None 0 8
2448.1.en \(\chi_{2448}(461, \cdot)\) None 0 8
2448.1.eq \(\chi_{2448}(43, \cdot)\) None 0 8
2448.1.er \(\chi_{2448}(77, \cdot)\) None 0 8
2448.1.eu \(\chi_{2448}(257, \cdot)\) None 0 8
2448.1.ev \(\chi_{2448}(223, \cdot)\) None 0 8
2448.1.ey \(\chi_{2448}(227, \cdot)\) None 0 16
2448.1.fb \(\chi_{2448}(61, \cdot)\) None 0 16
2448.1.fc \(\chi_{2448}(265, \cdot)\) None 0 16
2448.1.ff \(\chi_{2448}(23, \cdot)\) None 0 16
2448.1.fg \(\chi_{2448}(95, \cdot)\) None 0 16
2448.1.fj \(\chi_{2448}(97, \cdot)\) None 0 16
2448.1.fk \(\chi_{2448}(11, \cdot)\) None 0 16
2448.1.fn \(\chi_{2448}(301, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2448))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2448)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(612))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(816))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1224))\)\(^{\oplus 2}\)