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Properties

Label 3924.1
Level 3924
Weight 1
Dimension 248
Nonzero newspaces 13
Newform subspaces 22
Sturm bound 855360
Trace bound 13

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Defining parameters

Level: \( N \) = \( 3924 = 2^{2} \cdot 3^{2} \cdot 109 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 13 \)
Newform subspaces: \( 22 \)
Sturm bound: \(855360\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3924))\).

Total New Old
Modular forms 4962 1210 3752
Cusp forms 642 248 394
Eisenstein series 4320 962 3358

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 240 0 8 0

Trace form

\( 248 q + q^{2} + 7 q^{4} + q^{8} + 4 q^{9} + O(q^{10}) \) \( 248 q + q^{2} + 7 q^{4} + q^{8} + 4 q^{9} - 2 q^{10} - 8 q^{12} - 2 q^{13} + 7 q^{16} + 2 q^{17} + 4 q^{20} - 6 q^{22} - 5 q^{25} + 10 q^{26} + q^{32} - 2 q^{34} - 2 q^{37} - 2 q^{38} - 2 q^{40} + 2 q^{41} + 4 q^{45} + 10 q^{46} - 13 q^{49} + 3 q^{50} - 2 q^{52} + 2 q^{53} - 2 q^{58} + 4 q^{60} - 8 q^{61} + 7 q^{64} + 4 q^{65} + 2 q^{68} + 4 q^{73} + 2 q^{74} - 4 q^{78} - 4 q^{80} - 4 q^{81} + 6 q^{82} - 4 q^{85} + 6 q^{88} - 4 q^{89} + 18 q^{91} - 8 q^{93} - 6 q^{94} - 8 q^{97} + q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3924))\)

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
3924.1.d \(\chi_{3924}(1745, \cdot)\) None 0 1
3924.1.e \(\chi_{3924}(1961, \cdot)\) None 0 1
3924.1.f \(\chi_{3924}(1963, \cdot)\) None 0 1
3924.1.g \(\chi_{3924}(2179, \cdot)\) 3924.1.g.a 1 1
3924.1.g.b 1
3924.1.g.c 1
3924.1.g.d 1
3924.1.g.e 2
3924.1.g.f 2
3924.1.g.g 2
3924.1.g.h 2
3924.1.g.i 2
3924.1.g.j 4
3924.1.m \(\chi_{3924}(251, \cdot)\) 3924.1.m.a 4 2
3924.1.p \(\chi_{3924}(469, \cdot)\) None 0 2
3924.1.q \(\chi_{3924}(1589, \cdot)\) None 0 2
3924.1.r \(\chi_{3924}(173, \cdot)\) None 0 2
3924.1.u \(\chi_{3924}(391, \cdot)\) None 0 2
3924.1.v \(\chi_{3924}(1807, \cdot)\) None 0 2
3924.1.y \(\chi_{3924}(871, \cdot)\) 3924.1.y.a 8 2
3924.1.z \(\chi_{3924}(1027, \cdot)\) 3924.1.z.a 4 2
3924.1.ba \(\chi_{3924}(1135, \cdot)\) 3924.1.ba.a 2 2
3924.1.bb \(\chi_{3924}(655, \cdot)\) None 0 2
3924.1.bf \(\chi_{3924}(653, \cdot)\) None 0 2
3924.1.bg \(\chi_{3924}(809, \cdot)\) None 0 2
3924.1.bh \(\chi_{3924}(917, \cdot)\) None 0 2
3924.1.bi \(\chi_{3924}(437, \cdot)\) None 0 2
3924.1.bn \(\chi_{3924}(1481, \cdot)\) None 0 2
3924.1.bo \(\chi_{3924}(281, \cdot)\) None 0 2
3924.1.bq \(\chi_{3924}(499, \cdot)\) None 0 2
3924.1.br \(\chi_{3924}(1699, \cdot)\) None 0 2
3924.1.bw \(\chi_{3924}(695, \cdot)\) None 0 4
3924.1.by \(\chi_{3924}(613, \cdot)\) None 0 4
3924.1.bz \(\chi_{3924}(1057, \cdot)\) None 0 4
3924.1.cc \(\chi_{3924}(913, \cdot)\) None 0 4
3924.1.cd \(\chi_{3924}(335, \cdot)\) None 0 4
3924.1.cg \(\chi_{3924}(395, \cdot)\) 3924.1.cg.a 8 4
3924.1.ch \(\chi_{3924}(839, \cdot)\) None 0 4
3924.1.cj \(\chi_{3924}(553, \cdot)\) None 0 4
3924.1.co \(\chi_{3924}(1483, \cdot)\) None 0 6
3924.1.cp \(\chi_{3924}(2273, \cdot)\) None 0 6
3924.1.cq \(\chi_{3924}(845, \cdot)\) None 0 6
3924.1.cr \(\chi_{3924}(175, \cdot)\) None 0 6
3924.1.cs \(\chi_{3924}(343, \cdot)\) 3924.1.cs.a 6 6
3924.1.ct \(\chi_{3924}(113, \cdot)\) None 0 6
3924.1.cu \(\chi_{3924}(245, \cdot)\) None 0 6
3924.1.cv \(\chi_{3924}(1063, \cdot)\) 3924.1.cv.a 12 6
3924.1.cw \(\chi_{3924}(331, \cdot)\) None 0 6
3924.1.cx \(\chi_{3924}(125, \cdot)\) None 0 6
3924.1.cy \(\chi_{3924}(1265, \cdot)\) None 0 6
3924.1.cz \(\chi_{3924}(43, \cdot)\) None 0 6
3924.1.dk \(\chi_{3924}(637, \cdot)\) None 0 12
3924.1.dn \(\chi_{3924}(107, \cdot)\) 3924.1.dn.a 24 12
3924.1.do \(\chi_{3924}(419, \cdot)\) None 0 12
3924.1.dr \(\chi_{3924}(325, \cdot)\) None 0 12
3924.1.ds \(\chi_{3924}(241, \cdot)\) None 0 12
3924.1.du \(\chi_{3924}(23, \cdot)\) None 0 12
3924.1.dv \(\chi_{3924}(31, \cdot)\) None 0 18
3924.1.dw \(\chi_{3924}(353, \cdot)\) None 0 18
3924.1.eb \(\chi_{3924}(209, \cdot)\) None 0 18
3924.1.ec \(\chi_{3924}(307, \cdot)\) 3924.1.ec.a 18 18
3924.1.ed \(\chi_{3924}(197, \cdot)\) None 0 18
3924.1.ee \(\chi_{3924}(187, \cdot)\) None 0 18
3924.1.ej \(\chi_{3924}(5, \cdot)\) None 0 18
3924.1.ek \(\chi_{3924}(415, \cdot)\) 3924.1.ek.a 36 18
3924.1.el \(\chi_{3924}(89, \cdot)\) None 0 18
3924.1.em \(\chi_{3924}(211, \cdot)\) None 0 18
3924.1.en \(\chi_{3924}(7, \cdot)\) None 0 18
3924.1.eo \(\chi_{3924}(29, \cdot)\) None 0 18
3924.1.eq \(\chi_{3924}(59, \cdot)\) None 0 36
3924.1.er \(\chi_{3924}(133, \cdot)\) None 0 36
3924.1.ew \(\chi_{3924}(13, \cdot)\) None 0 36
3924.1.ex \(\chi_{3924}(179, \cdot)\) 3924.1.ex.a 72 36
3924.1.ey \(\chi_{3924}(37, \cdot)\) 3924.1.ey.a 36 36
3924.1.ez \(\chi_{3924}(11, \cdot)\) None 0 36

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3924))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3924)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(109))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(218))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(327))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(436))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(654))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(981))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1308))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1962))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3924))\)\(^{\oplus 1}\)