Properties

Label 3484.1
Level 3484
Weight 1
Dimension 72
Nonzero newspaces 5
Newform subspaces 8
Sturm bound 753984
Trace bound 2

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Defining parameters

Level: \( N \) = \( 3484 = 2^{2} \cdot 13 \cdot 67 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 8 \)
Sturm bound: \(753984\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3484))\).

Total New Old
Modular forms 4068 1504 2564
Cusp forms 108 72 36
Eisenstein series 3960 1432 2528

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 64 8 0 0

Trace form

\( 72q + 2q^{2} + 8q^{8} - 2q^{9} + O(q^{10}) \) \( 72q + 2q^{2} + 8q^{8} - 2q^{9} - 4q^{13} - 4q^{14} - 6q^{17} - 8q^{21} - 4q^{22} - 10q^{25} - 2q^{26} - 2q^{29} + 2q^{32} + 2q^{33} + 4q^{34} - 2q^{36} - 4q^{38} - 2q^{41} - 8q^{42} - 12q^{49} - 2q^{50} - 10q^{52} - 4q^{53} - 4q^{56} - 4q^{57} - 4q^{58} - 2q^{61} - 4q^{62} + 6q^{64} + 8q^{66} - 4q^{73} + 2q^{81} + 4q^{82} + 4q^{84} - 4q^{88} + 4q^{89} - 2q^{93} - 4q^{94} - 2q^{97} - 6q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3484))\)

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
3484.1.b \(\chi_{3484}(937, \cdot)\) None 0 1
3484.1.c \(\chi_{3484}(2547, \cdot)\) None 0 1
3484.1.d \(\chi_{3484}(1743, \cdot)\) None 0 1
3484.1.e \(\chi_{3484}(1741, \cdot)\) None 0 1
3484.1.o \(\chi_{3484}(1877, \cdot)\) None 0 2
3484.1.p \(\chi_{3484}(1071, \cdot)\) None 0 2
3484.1.q \(\chi_{3484}(3119, \cdot)\) 3484.1.q.a 2 2
3484.1.q.b 2
3484.1.r \(\chi_{3484}(105, \cdot)\) None 0 2
3484.1.s \(\chi_{3484}(909, \cdot)\) None 0 2
3484.1.t \(\chi_{3484}(2315, \cdot)\) None 0 2
3484.1.bd \(\chi_{3484}(633, \cdot)\) None 0 2
3484.1.be \(\chi_{3484}(2279, \cdot)\) None 0 2
3484.1.bf \(\chi_{3484}(439, \cdot)\) None 0 2
3484.1.bg \(\chi_{3484}(373, \cdot)\) None 0 2
3484.1.bh \(\chi_{3484}(133, \cdot)\) None 0 2
3484.1.bi \(\chi_{3484}(699, \cdot)\) None 0 2
3484.1.bj \(\chi_{3484}(1771, \cdot)\) 3484.1.bj.a 4 2
3484.1.bk \(\chi_{3484}(1473, \cdot)\) None 0 2
3484.1.bl \(\chi_{3484}(641, \cdot)\) None 0 2
3484.1.bm \(\chi_{3484}(1511, \cdot)\) 3484.1.bm.a 4 2
3484.1.bn \(\chi_{3484}(939, \cdot)\) None 0 2
3484.1.bo \(\chi_{3484}(901, \cdot)\) None 0 2
3484.1.bv \(\chi_{3484}(1571, \cdot)\) None 0 4
3484.1.bw \(\chi_{3484}(37, \cdot)\) None 0 4
3484.1.bx \(\chi_{3484}(297, \cdot)\) None 0 4
3484.1.by \(\chi_{3484}(267, \cdot)\) None 0 4
3484.1.bz \(\chi_{3484}(1073, \cdot)\) None 0 4
3484.1.ca \(\chi_{3484}(1311, \cdot)\) None 0 4
3484.1.ch \(\chi_{3484}(239, \cdot)\) None 0 4
3484.1.ci \(\chi_{3484}(2449, \cdot)\) None 0 4
3484.1.cm \(\chi_{3484}(857, \cdot)\) None 0 10
3484.1.cn \(\chi_{3484}(131, \cdot)\) None 0 10
3484.1.co \(\chi_{3484}(935, \cdot)\) 3484.1.co.a 10 10
3484.1.co.b 10
3484.1.cp \(\chi_{3484}(53, \cdot)\) None 0 10
3484.1.cu \(\chi_{3484}(187, \cdot)\) None 0 20
3484.1.cv \(\chi_{3484}(265, \cdot)\) None 0 20
3484.1.db \(\chi_{3484}(69, \cdot)\) None 0 20
3484.1.dc \(\chi_{3484}(107, \cdot)\) None 0 20
3484.1.dd \(\chi_{3484}(35, \cdot)\) None 0 20
3484.1.de \(\chi_{3484}(381, \cdot)\) None 0 20
3484.1.df \(\chi_{3484}(589, \cdot)\) None 0 20
3484.1.dg \(\chi_{3484}(55, \cdot)\) None 0 20
3484.1.dh \(\chi_{3484}(127, \cdot)\) None 0 20
3484.1.di \(\chi_{3484}(321, \cdot)\) None 0 20
3484.1.dj \(\chi_{3484}(113, \cdot)\) None 0 20
3484.1.dk \(\chi_{3484}(23, \cdot)\) None 0 20
3484.1.dl \(\chi_{3484}(283, \cdot)\) None 0 20
3484.1.dm \(\chi_{3484}(61, \cdot)\) None 0 20
3484.1.dw \(\chi_{3484}(183, \cdot)\) None 0 20
3484.1.dx \(\chi_{3484}(233, \cdot)\) None 0 20
3484.1.dy \(\chi_{3484}(677, \cdot)\) None 0 20
3484.1.dz \(\chi_{3484}(103, \cdot)\) 3484.1.dz.a 20 20
3484.1.dz.b 20
3484.1.ea \(\chi_{3484}(21, \cdot)\) None 0 40
3484.1.eb \(\chi_{3484}(31, \cdot)\) None 0 40
3484.1.ei \(\chi_{3484}(11, \cdot)\) None 0 40
3484.1.ej \(\chi_{3484}(89, \cdot)\) None 0 40
3484.1.ek \(\chi_{3484}(119, \cdot)\) None 0 40
3484.1.el \(\chi_{3484}(93, \cdot)\) None 0 40
3484.1.em \(\chi_{3484}(33, \cdot)\) None 0 40
3484.1.en \(\chi_{3484}(7, \cdot)\) None 0 40

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3484))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3484)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(268))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(871))\)\(^{\oplus 3}\)