Properties

Label 3420.1
Level 3420
Weight 1
Dimension 100
Nonzero newspaces 7
Newform subspaces 14
Sturm bound 622080
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 14 \)
Sturm bound: \(622080\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3420))\).

Total New Old
Modular forms 6476 1020 5456
Cusp forms 716 100 616
Eisenstein series 5760 920 4840

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 88 0 12 0

Trace form

\( 100 q + 4 q^{4} - 8 q^{7} + 4 q^{10} - 8 q^{11} - 2 q^{13} - 4 q^{16} + 2 q^{17} - 3 q^{19} - 8 q^{24} + 14 q^{25} + 3 q^{29} + 16 q^{30} + 4 q^{31} - 8 q^{34} + 3 q^{35} + 8 q^{36} - 4 q^{40} - 8 q^{43}+ \cdots - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3420))\)

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
3420.1.c \(\chi_{3420}(989, \cdot)\) None 0 1
3420.1.d \(\chi_{3420}(1711, \cdot)\) None 0 1
3420.1.g \(\chi_{3420}(2051, \cdot)\) None 0 1
3420.1.h \(\chi_{3420}(2089, \cdot)\) 3420.1.h.a 2 1
3420.1.h.b 4
3420.1.k \(\chi_{3420}(3079, \cdot)\) None 0 1
3420.1.l \(\chi_{3420}(3041, \cdot)\) None 0 1
3420.1.o \(\chi_{3420}(721, \cdot)\) None 0 1
3420.1.p \(\chi_{3420}(3419, \cdot)\) None 0 1
3420.1.u \(\chi_{3420}(2393, \cdot)\) 3420.1.u.a 8 2
3420.1.u.b 8
3420.1.w \(\chi_{3420}(1063, \cdot)\) None 0 2
3420.1.y \(\chi_{3420}(2053, \cdot)\) None 0 2
3420.1.ba \(\chi_{3420}(647, \cdot)\) None 0 2
3420.1.bd \(\chi_{3420}(1531, \cdot)\) None 0 2
3420.1.be \(\chi_{3420}(809, \cdot)\) None 0 2
3420.1.bh \(\chi_{3420}(829, \cdot)\) 3420.1.bh.a 2 2
3420.1.bi \(\chi_{3420}(791, \cdot)\) None 0 2
3420.1.bl \(\chi_{3420}(601, \cdot)\) None 0 2
3420.1.bm \(\chi_{3420}(2459, \cdot)\) None 0 2
3420.1.bn \(\chi_{3420}(1139, \cdot)\) 3420.1.bn.a 16 2
3420.1.bn.b 16
3420.1.bo \(\chi_{3420}(1741, \cdot)\) None 0 2
3420.1.bq \(\chi_{3420}(1861, \cdot)\) None 0 2
3420.1.bs \(\chi_{3420}(1019, \cdot)\) None 0 2
3420.1.bu \(\chi_{3420}(1759, \cdot)\) None 0 2
3420.1.bw \(\chi_{3420}(761, \cdot)\) None 0 2
3420.1.by \(\chi_{3420}(1721, \cdot)\) None 0 2
3420.1.bz \(\chi_{3420}(799, \cdot)\) None 0 2
3420.1.cb \(\chi_{3420}(619, \cdot)\) None 0 2
3420.1.cd \(\chi_{3420}(581, \cdot)\) None 0 2
3420.1.cg \(\chi_{3420}(3071, \cdot)\) None 0 2
3420.1.ci \(\chi_{3420}(949, \cdot)\) None 0 2
3420.1.ck \(\chi_{3420}(3109, \cdot)\) None 0 2
3420.1.cl \(\chi_{3420}(911, \cdot)\) None 0 2
3420.1.cn \(\chi_{3420}(1091, \cdot)\) None 0 2
3420.1.cp \(\chi_{3420}(1129, \cdot)\) None 0 2
3420.1.cs \(\chi_{3420}(1109, \cdot)\) None 0 2
3420.1.cu \(\chi_{3420}(1831, \cdot)\) None 0 2
3420.1.cw \(\chi_{3420}(571, \cdot)\) None 0 2
3420.1.cx \(\chi_{3420}(3089, \cdot)\) None 0 2
3420.1.cz \(\chi_{3420}(2129, \cdot)\) None 0 2
3420.1.db \(\chi_{3420}(391, \cdot)\) None 0 2
3420.1.de \(\chi_{3420}(881, \cdot)\) None 0 2
3420.1.df \(\chi_{3420}(919, \cdot)\) 3420.1.df.a 4 2
3420.1.df.b 4
3420.1.dh \(\chi_{3420}(179, \cdot)\) None 0 2
3420.1.di \(\chi_{3420}(901, \cdot)\) None 0 2
3420.1.do \(\chi_{3420}(487, \cdot)\) None 0 4
3420.1.dq \(\chi_{3420}(1133, \cdot)\) None 0 4
3420.1.dr \(\chi_{3420}(277, \cdot)\) None 0 4
3420.1.dv \(\chi_{3420}(83, \cdot)\) None 0 4
3420.1.dw \(\chi_{3420}(1103, \cdot)\) None 0 4
3420.1.dz \(\chi_{3420}(733, \cdot)\) None 0 4
3420.1.ea \(\chi_{3420}(457, \cdot)\) None 0 4
3420.1.eb \(\chi_{3420}(2063, \cdot)\) None 0 4
3420.1.ed \(\chi_{3420}(1433, \cdot)\) None 0 4
3420.1.eh \(\chi_{3420}(103, \cdot)\) None 0 4
3420.1.ei \(\chi_{3420}(607, \cdot)\) None 0 4
3420.1.el \(\chi_{3420}(293, \cdot)\) None 0 4
3420.1.em \(\chi_{3420}(113, \cdot)\) None 0 4
3420.1.en \(\chi_{3420}(2083, \cdot)\) None 0 4
3420.1.eq \(\chi_{3420}(467, \cdot)\) None 0 4
3420.1.es \(\chi_{3420}(577, \cdot)\) 3420.1.es.a 4 4
3420.1.es.b 4
3420.1.es.c 4
3420.1.eu \(\chi_{3420}(851, \cdot)\) None 0 6
3420.1.ev \(\chi_{3420}(409, \cdot)\) None 0 6
3420.1.ey \(\chi_{3420}(329, \cdot)\) None 0 6
3420.1.ez \(\chi_{3420}(511, \cdot)\) None 0 6
3420.1.fb \(\chi_{3420}(499, \cdot)\) None 0 6
3420.1.fe \(\chi_{3420}(101, \cdot)\) None 0 6
3420.1.ff \(\chi_{3420}(1079, \cdot)\) None 0 6
3420.1.fg \(\chi_{3420}(181, \cdot)\) None 0 6
3420.1.fj \(\chi_{3420}(161, \cdot)\) None 0 6
3420.1.fk \(\chi_{3420}(199, \cdot)\) 3420.1.fk.a 12 6
3420.1.fk.b 12
3420.1.fm \(\chi_{3420}(241, \cdot)\) None 0 6
3420.1.fo \(\chi_{3420}(59, \cdot)\) None 0 6
3420.1.fq \(\chi_{3420}(1051, \cdot)\) None 0 6
3420.1.fr \(\chi_{3420}(149, \cdot)\) None 0 6
3420.1.ft \(\chi_{3420}(71, \cdot)\) None 0 6
3420.1.fw \(\chi_{3420}(109, \cdot)\) None 0 6
3420.1.fx \(\chi_{3420}(1529, \cdot)\) None 0 6
3420.1.ga \(\chi_{3420}(271, \cdot)\) None 0 6
3420.1.gc \(\chi_{3420}(889, \cdot)\) None 0 6
3420.1.gd \(\chi_{3420}(371, \cdot)\) None 0 6
3420.1.gf \(\chi_{3420}(299, \cdot)\) None 0 6
3420.1.gh \(\chi_{3420}(421, \cdot)\) None 0 6
3420.1.gi \(\chi_{3420}(461, \cdot)\) None 0 6
3420.1.gl \(\chi_{3420}(139, \cdot)\) None 0 6
3420.1.gn \(\chi_{3420}(317, \cdot)\) None 0 12
3420.1.gp \(\chi_{3420}(547, \cdot)\) None 0 12
3420.1.gr \(\chi_{3420}(517, \cdot)\) None 0 12
3420.1.gt \(\chi_{3420}(73, \cdot)\) None 0 12
3420.1.gv \(\chi_{3420}(23, \cdot)\) None 0 12
3420.1.gx \(\chi_{3420}(503, \cdot)\) None 0 12
3420.1.gz \(\chi_{3420}(67, \cdot)\) None 0 12
3420.1.hb \(\chi_{3420}(127, \cdot)\) None 0 12
3420.1.hd \(\chi_{3420}(173, \cdot)\) None 0 12
3420.1.hf \(\chi_{3420}(53, \cdot)\) None 0 12
3420.1.hh \(\chi_{3420}(47, \cdot)\) None 0 12
3420.1.hj \(\chi_{3420}(157, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3420))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3420)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(570))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(684))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(855))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1710))\)\(^{\oplus 2}\)