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Properties

Label 3104.1
Level 3104
Weight 1
Dimension 107
Nonzero newspaces 12
Newform subspaces 15
Sturm bound 602112
Trace bound 11

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Defining parameters

Level: \( N \) = \( 3104 = 2^{5} \cdot 97 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 15 \)
Sturm bound: \(602112\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3104))\).

Total New Old
Modular forms 3496 1057 2439
Cusp forms 424 107 317
Eisenstein series 3072 950 2122

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 103 4 0 0

Trace form

\( 107 q + 6 q^{3} + 2 q^{5} + q^{9} + O(q^{10}) \) \( 107 q + 6 q^{3} + 2 q^{5} + q^{9} + 2 q^{11} - 2 q^{13} + 2 q^{19} - 2 q^{21} + 7 q^{25} + 12 q^{27} - 2 q^{29} + 4 q^{35} - 2 q^{37} + 2 q^{43} + 7 q^{49} + 4 q^{51} + 2 q^{53} + 2 q^{59} + 2 q^{61} - 2 q^{65} + 2 q^{67} + 4 q^{69} - 8 q^{73} + 6 q^{75} - 4 q^{77} - 3 q^{81} + 2 q^{83} + 4 q^{85} - 14 q^{89} + 4 q^{91} - 2 q^{93} - 5 q^{97} + 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3104))\)

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
3104.1.b \(\chi_{3104}(3103, \cdot)\) None 0 1
3104.1.e \(\chi_{3104}(2911, \cdot)\) None 0 1
3104.1.g \(\chi_{3104}(1359, \cdot)\) None 0 1
3104.1.h \(\chi_{3104}(1551, \cdot)\) 3104.1.h.a 1 1
3104.1.h.b 2
3104.1.h.c 2
3104.1.h.d 4
3104.1.k \(\chi_{3104}(463, \cdot)\) 3104.1.k.a 2 2
3104.1.l \(\chi_{3104}(1239, \cdot)\) None 0 2
3104.1.n \(\chi_{3104}(775, \cdot)\) None 0 2
3104.1.q \(\chi_{3104}(583, \cdot)\) None 0 2
3104.1.s \(\chi_{3104}(119, \cdot)\) None 0 2
3104.1.u \(\chi_{3104}(895, \cdot)\) None 0 2
3104.1.v \(\chi_{3104}(1103, \cdot)\) 3104.1.v.a 2 2
3104.1.w \(\chi_{3104}(1199, \cdot)\) 3104.1.w.a 2 2
3104.1.y \(\chi_{3104}(255, \cdot)\) 3104.1.y.a 4 2
3104.1.bb \(\chi_{3104}(159, \cdot)\) None 0 2
3104.1.bd \(\chi_{3104}(2087, \cdot)\) None 0 4
3104.1.be \(\chi_{3104}(355, \cdot)\) None 0 4
3104.1.bh \(\chi_{3104}(507, \cdot)\) None 0 4
3104.1.bj \(\chi_{3104}(1311, \cdot)\) None 0 4
3104.1.bl \(\chi_{3104}(47, \cdot)\) 3104.1.bl.a 4 4
3104.1.bn \(\chi_{3104}(147, \cdot)\) None 0 4
3104.1.bp \(\chi_{3104}(387, \cdot)\) None 0 4
3104.1.bq \(\chi_{3104}(195, \cdot)\) None 0 4
3104.1.bs \(\chi_{3104}(435, \cdot)\) None 0 4
3104.1.bv \(\chi_{3104}(75, \cdot)\) None 0 4
3104.1.bw \(\chi_{3104}(227, \cdot)\) None 0 4
3104.1.bz \(\chi_{3104}(535, \cdot)\) None 0 4
3104.1.ca \(\chi_{3104}(479, \cdot)\) None 0 4
3104.1.cd \(\chi_{3104}(103, \cdot)\) None 0 4
3104.1.ce \(\chi_{3104}(423, \cdot)\) None 0 4
3104.1.ch \(\chi_{3104}(327, \cdot)\) None 0 4
3104.1.ci \(\chi_{3104}(695, \cdot)\) None 0 4
3104.1.ck \(\chi_{3104}(879, \cdot)\) 3104.1.ck.a 4 4
3104.1.cn \(\chi_{3104}(555, \cdot)\) None 0 8
3104.1.co \(\chi_{3104}(283, \cdot)\) None 0 8
3104.1.cr \(\chi_{3104}(299, \cdot)\) None 0 8
3104.1.ct \(\chi_{3104}(415, \cdot)\) None 0 8
3104.1.cu \(\chi_{3104}(167, \cdot)\) None 0 8
3104.1.cx \(\chi_{3104}(279, \cdot)\) None 0 8
3104.1.cy \(\chi_{3104}(79, \cdot)\) 3104.1.cy.a 8 8
3104.1.da \(\chi_{3104}(27, \cdot)\) None 0 8
3104.1.dd \(\chi_{3104}(151, \cdot)\) None 0 8
3104.1.de \(\chi_{3104}(43, \cdot)\) None 0 8
3104.1.dg \(\chi_{3104}(275, \cdot)\) None 0 8
3104.1.di \(\chi_{3104}(267, \cdot)\) None 0 8
3104.1.dl \(\chi_{3104}(35, \cdot)\) None 0 8
3104.1.dm \(\chi_{3104}(547, \cdot)\) None 0 8
3104.1.dp \(\chi_{3104}(203, \cdot)\) None 0 8
3104.1.dr \(\chi_{3104}(431, \cdot)\) 3104.1.dr.a 8 8
3104.1.dt \(\chi_{3104}(287, \cdot)\) None 0 8
3104.1.du \(\chi_{3104}(91, \cdot)\) None 0 8
3104.1.dw \(\chi_{3104}(1043, \cdot)\) None 0 8
3104.1.dz \(\chi_{3104}(295, \cdot)\) None 0 8
3104.1.ea \(\chi_{3104}(337, \cdot)\) None 0 16
3104.1.ed \(\chi_{3104}(213, \cdot)\) None 0 16
3104.1.ee \(\chi_{3104}(249, \cdot)\) None 0 16
3104.1.eg \(\chi_{3104}(893, \cdot)\) None 0 16
3104.1.ei \(\chi_{3104}(45, \cdot)\) None 0 16
3104.1.ek \(\chi_{3104}(457, \cdot)\) None 0 16
3104.1.em \(\chi_{3104}(117, \cdot)\) None 0 16
3104.1.ep \(\chi_{3104}(257, \cdot)\) 3104.1.ep.a 16 16
3104.1.er \(\chi_{3104}(3, \cdot)\) None 0 16
3104.1.et \(\chi_{3104}(335, \cdot)\) 3104.1.et.a 16 16
3104.1.eu \(\chi_{3104}(247, \cdot)\) None 0 16
3104.1.ex \(\chi_{3104}(183, \cdot)\) None 0 16
3104.1.ey \(\chi_{3104}(31, \cdot)\) None 0 16
3104.1.fb \(\chi_{3104}(11, \cdot)\) None 0 16
3104.1.fc \(\chi_{3104}(99, \cdot)\) None 0 16
3104.1.fe \(\chi_{3104}(163, \cdot)\) None 0 16
3104.1.fg \(\chi_{3104}(417, \cdot)\) 3104.1.fg.a 32 32
3104.1.fj \(\chi_{3104}(5, \cdot)\) None 0 32
3104.1.fl \(\chi_{3104}(41, \cdot)\) None 0 32
3104.1.fn \(\chi_{3104}(37, \cdot)\) None 0 32
3104.1.fp \(\chi_{3104}(13, \cdot)\) None 0 32
3104.1.fr \(\chi_{3104}(137, \cdot)\) None 0 32
3104.1.fs \(\chi_{3104}(165, \cdot)\) None 0 32
3104.1.fv \(\chi_{3104}(17, \cdot)\) None 0 32

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3104))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3104)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(388))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(776))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1552))\)\(^{\oplus 2}\)