Properties

Label 3311.1
Level 3311
Weight 1
Dimension 406
Nonzero newspaces 11
Newforms 36
Sturm bound 887040
Trace bound 2

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Defining parameters

Level: \( N \) = \( 3311 = 7 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 11 \)
Newforms: \( 36 \)
Sturm bound: \(887040\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3311))\).

Total New Old
Modular forms 5510 4098 1412
Cusp forms 470 406 64
Eisenstein series 5040 3692 1348

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 406 0 0 0

Trace form

\(406q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 30q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(406q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 30q^{9} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 12q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 12q^{16} \) \(\mathstrut -\mathstrut 6q^{18} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 30q^{25} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 4q^{29} \) \(\mathstrut -\mathstrut 50q^{32} \) \(\mathstrut +\mathstrut 30q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 52q^{56} \) \(\mathstrut -\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 2q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 6q^{71} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 34q^{74} \) \(\mathstrut +\mathstrut 2q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 6q^{79} \) \(\mathstrut +\mathstrut 30q^{81} \) \(\mathstrut -\mathstrut 39q^{86} \) \(\mathstrut -\mathstrut 23q^{88} \) \(\mathstrut -\mathstrut 8q^{92} \) \(\mathstrut +\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3311))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3311.1.b \(\chi_{3311}(386, \cdot)\) None 0 1
3311.1.d \(\chi_{3311}(1506, \cdot)\) None 0 1
3311.1.f \(\chi_{3311}(1420, \cdot)\) None 0 1
3311.1.h \(\chi_{3311}(3310, \cdot)\) 3311.1.h.a 1 1
3311.1.h.b 1
3311.1.h.c 1
3311.1.h.d 1
3311.1.h.e 1
3311.1.h.f 1
3311.1.h.g 2
3311.1.h.h 2
3311.1.h.i 2
3311.1.h.j 2
3311.1.h.k 3
3311.1.h.l 3
3311.1.h.m 3
3311.1.h.n 3
3311.1.h.o 6
3311.1.h.p 6
3311.1.o \(\chi_{3311}(2199, \cdot)\) None 0 2
3311.1.q \(\chi_{3311}(2157, \cdot)\) None 0 2
3311.1.s \(\chi_{3311}(122, \cdot)\) None 0 2
3311.1.t \(\chi_{3311}(472, \cdot)\) None 0 2
3311.1.u \(\chi_{3311}(824, \cdot)\) None 0 2
3311.1.v \(\chi_{3311}(2014, \cdot)\) None 0 2
3311.1.y \(\chi_{3311}(474, \cdot)\) None 0 2
3311.1.z \(\chi_{3311}(1671, \cdot)\) None 0 2
3311.1.bb \(\chi_{3311}(639, \cdot)\) None 0 2
3311.1.bd \(\chi_{3311}(1033, \cdot)\) None 0 2
3311.1.be \(\chi_{3311}(681, \cdot)\) None 0 2
3311.1.bg \(\chi_{3311}(2531, \cdot)\) None 0 2
3311.1.bj \(\chi_{3311}(1332, \cdot)\) None 0 2
3311.1.bl \(\chi_{3311}(2573, \cdot)\) None 0 2
3311.1.bm \(\chi_{3311}(1770, \cdot)\) 3311.1.bm.a 2 2
3311.1.bm.b 2
3311.1.bo \(\chi_{3311}(2113, \cdot)\) None 0 2
3311.1.bq \(\chi_{3311}(601, \cdot)\) 3311.1.bq.a 4 4
3311.1.bq.b 4
3311.1.bs \(\chi_{3311}(818, \cdot)\) None 0 4
3311.1.bu \(\chi_{3311}(904, \cdot)\) None 0 4
3311.1.bw \(\chi_{3311}(687, \cdot)\) None 0 4
3311.1.bx \(\chi_{3311}(538, \cdot)\) 3311.1.bx.a 6 6
3311.1.bx.b 6
3311.1.bz \(\chi_{3311}(188, \cdot)\) None 0 6
3311.1.cb \(\chi_{3311}(274, \cdot)\) None 0 6
3311.1.cd \(\chi_{3311}(309, \cdot)\) None 0 6
3311.1.cm \(\chi_{3311}(251, \cdot)\) 3311.1.cm.a 8 8
3311.1.cm.b 8
3311.1.co \(\chi_{3311}(811, \cdot)\) 3311.1.co.a 8 8
3311.1.co.b 8
3311.1.cp \(\chi_{3311}(436, \cdot)\) None 0 8
3311.1.cr \(\chi_{3311}(214, \cdot)\) None 0 8
3311.1.cu \(\chi_{3311}(93, \cdot)\) None 0 8
3311.1.cw \(\chi_{3311}(79, \cdot)\) None 0 8
3311.1.cx \(\chi_{3311}(431, \cdot)\) None 0 8
3311.1.cz \(\chi_{3311}(37, \cdot)\) None 0 8
3311.1.db \(\chi_{3311}(437, \cdot)\) None 0 8
3311.1.dc \(\chi_{3311}(388, \cdot)\) None 0 8
3311.1.df \(\chi_{3311}(509, \cdot)\) None 0 8
3311.1.dg \(\chi_{3311}(222, \cdot)\) None 0 8
3311.1.dh \(\chi_{3311}(171, \cdot)\) None 0 8
3311.1.di \(\chi_{3311}(423, \cdot)\) None 0 8
3311.1.dk \(\chi_{3311}(295, \cdot)\) None 0 8
3311.1.dm \(\chi_{3311}(337, \cdot)\) None 0 8
3311.1.dp \(\chi_{3311}(111, \cdot)\) None 0 12
3311.1.dr \(\chi_{3311}(76, \cdot)\) 3311.1.dr.a 12 12
3311.1.dr.b 12
3311.1.ds \(\chi_{3311}(186, \cdot)\) None 0 12
3311.1.du \(\chi_{3311}(254, \cdot)\) None 0 12
3311.1.dx \(\chi_{3311}(331, \cdot)\) None 0 12
3311.1.dz \(\chi_{3311}(109, \cdot)\) None 0 12
3311.1.ea \(\chi_{3311}(219, \cdot)\) None 0 12
3311.1.ec \(\chi_{3311}(177, \cdot)\) None 0 12
3311.1.ee \(\chi_{3311}(241, \cdot)\) None 0 12
3311.1.ef \(\chi_{3311}(551, \cdot)\) None 0 12
3311.1.ei \(\chi_{3311}(705, \cdot)\) None 0 12
3311.1.ej \(\chi_{3311}(362, \cdot)\) None 0 12
3311.1.ek \(\chi_{3311}(131, \cdot)\) None 0 12
3311.1.el \(\chi_{3311}(353, \cdot)\) None 0 12
3311.1.en \(\chi_{3311}(155, \cdot)\) None 0 12
3311.1.ep \(\chi_{3311}(197, \cdot)\) None 0 12
3311.1.er \(\chi_{3311}(113, \cdot)\) None 0 24
3311.1.et \(\chi_{3311}(127, \cdot)\) None 0 24
3311.1.ev \(\chi_{3311}(97, \cdot)\) 3311.1.ev.a 24 24
3311.1.ev.b 24
3311.1.ex \(\chi_{3311}(118, \cdot)\) 3311.1.ex.a 24 24
3311.1.ex.b 24
3311.1.fd \(\chi_{3311}(57, \cdot)\) None 0 48
3311.1.ff \(\chi_{3311}(71, \cdot)\) None 0 48
3311.1.fh \(\chi_{3311}(124, \cdot)\) None 0 48
3311.1.fi \(\chi_{3311}(94, \cdot)\) None 0 48
3311.1.fj \(\chi_{3311}(61, \cdot)\) None 0 48
3311.1.fk \(\chi_{3311}(31, \cdot)\) None 0 48
3311.1.fn \(\chi_{3311}(47, \cdot)\) None 0 48
3311.1.fo \(\chi_{3311}(19, \cdot)\) None 0 48
3311.1.fq \(\chi_{3311}(158, \cdot)\) None 0 48
3311.1.fs \(\chi_{3311}(107, \cdot)\) None 0 48
3311.1.ft \(\chi_{3311}(74, \cdot)\) None 0 48
3311.1.fv \(\chi_{3311}(114, \cdot)\) None 0 48
3311.1.fy \(\chi_{3311}(137, \cdot)\) None 0 48
3311.1.ga \(\chi_{3311}(95, \cdot)\) None 0 48
3311.1.gb \(\chi_{3311}(62, \cdot)\) 3311.1.gb.a 48 48
3311.1.gb.b 48
3311.1.gd \(\chi_{3311}(146, \cdot)\) 3311.1.gd.a 48 48
3311.1.gd.b 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3311))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3311)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(301))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(473))\)\(^{\oplus 2}\)