↑

Properties

Label 3312.1
Level 3312
Weight 1
Dimension 61
Nonzero newspaces 5
Newform subspaces 8
Sturm bound 608256
Trace bound 23

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 8 \)
Sturm bound: \(608256\)
Trace bound: \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3312))\).

Total New Old
Modular forms 5278 912 4366
Cusp forms 350 61 289
Eisenstein series 4928 851 4077

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 61 0 0 0

Trace form

\( 61 q - q^{13} + 4 q^{23} - 2 q^{25} + 3 q^{27} + q^{29} + q^{31} - 12 q^{36} + 15 q^{39} + q^{41} - q^{47} - 8 q^{49} + 6 q^{58} + 17 q^{59} - 18 q^{62} + 18 q^{64} - q^{71} - q^{73} - 12 q^{78}+ \cdots + 9 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3312))\)

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
3312.1.c \(\chi_{3312}(2161, \cdot)\) 3312.1.c.a 1 1
3312.1.d \(\chi_{3312}(2071, \cdot)\) None 0 1
3312.1.g \(\chi_{3312}(737, \cdot)\) None 0 1
3312.1.h \(\chi_{3312}(1655, \cdot)\) None 0 1
3312.1.k \(\chi_{3312}(415, \cdot)\) None 0 1
3312.1.l \(\chi_{3312}(505, \cdot)\) None 0 1
3312.1.o \(\chi_{3312}(3311, \cdot)\) None 0 1
3312.1.p \(\chi_{3312}(2393, \cdot)\) None 0 1
3312.1.s \(\chi_{3312}(1565, \cdot)\) None 0 2
3312.1.t \(\chi_{3312}(827, \cdot)\) None 0 2
3312.1.w \(\chi_{3312}(1333, \cdot)\) 3312.1.w.a 2 2
3312.1.w.b 4
3312.1.x \(\chi_{3312}(1243, \cdot)\) None 0 2
3312.1.z \(\chi_{3312}(185, \cdot)\) None 0 2
3312.1.ba \(\chi_{3312}(1103, \cdot)\) None 0 2
3312.1.bd \(\chi_{3312}(1609, \cdot)\) None 0 2
3312.1.be \(\chi_{3312}(1519, \cdot)\) None 0 2
3312.1.bh \(\chi_{3312}(551, \cdot)\) None 0 2
3312.1.bi \(\chi_{3312}(1841, \cdot)\) None 0 2
3312.1.bl \(\chi_{3312}(967, \cdot)\) None 0 2
3312.1.bm \(\chi_{3312}(1057, \cdot)\) 3312.1.bm.a 6 2
3312.1.bp \(\chi_{3312}(229, \cdot)\) 3312.1.bp.a 12 4
3312.1.bp.b 12
3312.1.bs \(\chi_{3312}(139, \cdot)\) None 0 4
3312.1.bt \(\chi_{3312}(461, \cdot)\) None 0 4
3312.1.bw \(\chi_{3312}(275, \cdot)\) 3312.1.bw.a 12 4
3312.1.bw.b 12
3312.1.bx \(\chi_{3312}(233, \cdot)\) None 0 10
3312.1.by \(\chi_{3312}(143, \cdot)\) None 0 10
3312.1.cb \(\chi_{3312}(217, \cdot)\) None 0 10
3312.1.cc \(\chi_{3312}(127, \cdot)\) None 0 10
3312.1.cf \(\chi_{3312}(359, \cdot)\) None 0 10
3312.1.cg \(\chi_{3312}(305, \cdot)\) None 0 10
3312.1.cj \(\chi_{3312}(55, \cdot)\) None 0 10
3312.1.ck \(\chi_{3312}(145, \cdot)\) None 0 10
3312.1.co \(\chi_{3312}(163, \cdot)\) None 0 20
3312.1.cp \(\chi_{3312}(37, \cdot)\) None 0 20
3312.1.cs \(\chi_{3312}(107, \cdot)\) None 0 20
3312.1.ct \(\chi_{3312}(197, \cdot)\) None 0 20
3312.1.cw \(\chi_{3312}(97, \cdot)\) None 0 20
3312.1.cx \(\chi_{3312}(151, \cdot)\) None 0 20
3312.1.da \(\chi_{3312}(209, \cdot)\) None 0 20
3312.1.db \(\chi_{3312}(263, \cdot)\) None 0 20
3312.1.de \(\chi_{3312}(31, \cdot)\) None 0 20
3312.1.df \(\chi_{3312}(313, \cdot)\) None 0 20
3312.1.di \(\chi_{3312}(191, \cdot)\) None 0 20
3312.1.dj \(\chi_{3312}(41, \cdot)\) None 0 20
3312.1.dk \(\chi_{3312}(11, \cdot)\) None 0 40
3312.1.dn \(\chi_{3312}(29, \cdot)\) None 0 40
3312.1.do \(\chi_{3312}(187, \cdot)\) None 0 40
3312.1.dr \(\chi_{3312}(61, \cdot)\) None 0 40

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3312))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3312)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 15}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(828))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1656))\)\(^{\oplus 2}\)