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Properties

Label 3479.1
Level 3479
Weight 1
Dimension 256
Nonzero newspaces 11
Newform subspaces 23
Sturm bound 987840
Trace bound 9

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Defining parameters

Level: \( N \) = \( 3479 = 7^{2} \cdot 71 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 11 \)
Newform subspaces: \( 23 \)
Sturm bound: \(987840\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3479))\).

Total New Old
Modular forms 4541 3603 938
Cusp forms 341 256 85
Eisenstein series 4200 3347 853

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 248 8 0 0

Trace form

\( 256 q + 5 q^{2} - q^{3} + q^{4} + 3 q^{5} + 6 q^{6} - 38 q^{8} - q^{9} + O(q^{10}) \) \( 256 q + 5 q^{2} - q^{3} + q^{4} + 3 q^{5} + 6 q^{6} - 38 q^{8} - q^{9} + 4 q^{10} + 2 q^{11} + 3 q^{12} - 18 q^{15} + 2 q^{16} - 2 q^{18} - q^{19} - 4 q^{20} - 8 q^{22} + 2 q^{23} - q^{24} - q^{25} - 2 q^{27} - 3 q^{29} - 5 q^{30} + 9 q^{32} + 61 q^{36} + 5 q^{37} - 7 q^{38} + 2 q^{40} - 15 q^{43} + 6 q^{44} + 3 q^{45} + 4 q^{46} - 6 q^{48} - 13 q^{50} + 2 q^{53} + 6 q^{54} - 2 q^{57} + 6 q^{58} - q^{60} + 36 q^{64} + 2 q^{67} - 11 q^{71} + 3 q^{72} + 3 q^{73} + q^{74} - 4 q^{75} + 3 q^{76} + q^{79} - 4 q^{80} - 2 q^{81} + q^{83} + 6 q^{86} - 5 q^{87} - 27 q^{88} - q^{89} - q^{90} - 12 q^{92} - q^{96} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3479))\)

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
3479.1.c \(\chi_{3479}(2841, \cdot)\) None 0 1
3479.1.d \(\chi_{3479}(638, \cdot)\) 3479.1.d.a 1 1
3479.1.d.b 2
3479.1.d.c 2
3479.1.d.d 2
3479.1.d.e 3
3479.1.d.f 6
3479.1.d.g 12
3479.1.g \(\chi_{3479}(851, \cdot)\) 3479.1.g.a 2 2
3479.1.g.b 4
3479.1.g.c 4
3479.1.g.d 6
3479.1.g.e 6
3479.1.g.f 12
3479.1.g.g 24
3479.1.h \(\chi_{3479}(2273, \cdot)\) None 0 2
3479.1.r \(\chi_{3479}(1079, \cdot)\) 3479.1.r.a 4 4
3479.1.s \(\chi_{3479}(1567, \cdot)\) None 0 4
3479.1.u \(\chi_{3479}(258, \cdot)\) None 0 6
3479.1.w \(\chi_{3479}(176, \cdot)\) None 0 6
3479.1.x \(\chi_{3479}(141, \cdot)\) None 0 6
3479.1.y \(\chi_{3479}(239, \cdot)\) None 0 6
3479.1.z \(\chi_{3479}(680, \cdot)\) None 0 6
3479.1.ba \(\chi_{3479}(449, \cdot)\) None 0 6
3479.1.bb \(\chi_{3479}(736, \cdot)\) 3479.1.bb.a 6 6
3479.1.bc \(\chi_{3479}(48, \cdot)\) None 0 6
3479.1.be \(\chi_{3479}(314, \cdot)\) None 0 6
3479.1.bg \(\chi_{3479}(20, \cdot)\) None 0 6
3479.1.bj \(\chi_{3479}(517, \cdot)\) None 0 6
3479.1.bk \(\chi_{3479}(356, \cdot)\) None 0 6
3479.1.bn \(\chi_{3479}(1511, \cdot)\) None 0 6
3479.1.bo \(\chi_{3479}(974, \cdot)\) None 0 6
3479.1.bp \(\chi_{3479}(820, \cdot)\) None 0 6
3479.1.bq \(\chi_{3479}(545, \cdot)\) None 0 6
3479.1.cc \(\chi_{3479}(999, \cdot)\) 3479.1.cc.a 8 8
3479.1.cd \(\chi_{3479}(1292, \cdot)\) 3479.1.cd.a 8 8
3479.1.cn \(\chi_{3479}(250, \cdot)\) None 0 12
3479.1.co \(\chi_{3479}(389, \cdot)\) None 0 12
3479.1.cp \(\chi_{3479}(254, \cdot)\) None 0 12
3479.1.cr \(\chi_{3479}(45, \cdot)\) None 0 12
3479.1.cs \(\chi_{3479}(187, \cdot)\) None 0 12
3479.1.cv \(\chi_{3479}(143, \cdot)\) None 0 12
3479.1.cw \(\chi_{3479}(101, \cdot)\) None 0 12
3479.1.cz \(\chi_{3479}(332, \cdot)\) None 0 12
3479.1.db \(\chi_{3479}(1097, \cdot)\) 3479.1.db.a 12 12
3479.1.dc \(\chi_{3479}(165, \cdot)\) 3479.1.dc.a 12 12
3479.1.dd \(\chi_{3479}(744, \cdot)\) None 0 12
3479.1.de \(\chi_{3479}(247, \cdot)\) None 0 12
3479.1.df \(\chi_{3479}(212, \cdot)\) None 0 12
3479.1.dg \(\chi_{3479}(23, \cdot)\) None 0 12
3479.1.dh \(\chi_{3479}(51, \cdot)\) None 0 12
3479.1.dj \(\chi_{3479}(103, \cdot)\) None 0 12
3479.1.dl \(\chi_{3479}(160, \cdot)\) None 0 24
3479.1.dm \(\chi_{3479}(113, \cdot)\) None 0 24
3479.1.dn \(\chi_{3479}(78, \cdot)\) None 0 24
3479.1.do \(\chi_{3479}(27, \cdot)\) None 0 24
3479.1.dr \(\chi_{3479}(76, \cdot)\) None 0 24
3479.1.ds \(\chi_{3479}(202, \cdot)\) None 0 24
3479.1.dv \(\chi_{3479}(6, \cdot)\) None 0 24
3479.1.dx \(\chi_{3479}(363, \cdot)\) None 0 24
3479.1.dz \(\chi_{3479}(146, \cdot)\) None 0 24
3479.1.ea \(\chi_{3479}(99, \cdot)\) 3479.1.ea.a 24 24
3479.1.eb \(\chi_{3479}(92, \cdot)\) None 0 24
3479.1.ec \(\chi_{3479}(22, \cdot)\) None 0 24
3479.1.ed \(\chi_{3479}(155, \cdot)\) None 0 24
3479.1.ee \(\chi_{3479}(85, \cdot)\) None 0 24
3479.1.ef \(\chi_{3479}(134, \cdot)\) None 0 24
3479.1.eh \(\chi_{3479}(90, \cdot)\) None 0 24
3479.1.eq \(\chi_{3479}(40, \cdot)\) None 0 48
3479.1.es \(\chi_{3479}(44, \cdot)\) None 0 48
3479.1.et \(\chi_{3479}(207, \cdot)\) None 0 48
3479.1.eu \(\chi_{3479}(46, \cdot)\) None 0 48
3479.1.ev \(\chi_{3479}(305, \cdot)\) None 0 48
3479.1.ew \(\chi_{3479}(53, \cdot)\) None 0 48
3479.1.ex \(\chi_{3479}(67, \cdot)\) 3479.1.ex.a 48 48
3479.1.ey \(\chi_{3479}(19, \cdot)\) 3479.1.ey.a 48 48
3479.1.fa \(\chi_{3479}(38, \cdot)\) None 0 48
3479.1.fd \(\chi_{3479}(75, \cdot)\) None 0 48
3479.1.fe \(\chi_{3479}(5, \cdot)\) None 0 48
3479.1.fh \(\chi_{3479}(3, \cdot)\) None 0 48
3479.1.fi \(\chi_{3479}(10, \cdot)\) None 0 48
3479.1.fk \(\chi_{3479}(11, \cdot)\) None 0 48
3479.1.fl \(\chi_{3479}(102, \cdot)\) None 0 48
3479.1.fm \(\chi_{3479}(12, \cdot)\) None 0 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3479))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3479)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(71))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(497))\)\(^{\oplus 2}\)