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Properties

Label 2793.1
Level 2793
Weight 1
Dimension 298
Nonzero newspaces 19
Newform subspaces 35
Sturm bound 564480
Trace bound 43

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Defining parameters

Level: \( N \) = \( 2793 = 3 \cdot 7^{2} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 19 \)
Newform subspaces: \( 35 \)
Sturm bound: \(564480\)
Trace bound: \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2793))\).

Total New Old
Modular forms 4804 1946 2858
Cusp forms 484 298 186
Eisenstein series 4320 1648 2672

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 282 16 0 0

Trace form

\( 298 q + 3 q^{3} - q^{4} - 4 q^{6} + 2 q^{7} + q^{9} + O(q^{10}) \) \( 298 q + 3 q^{3} - q^{4} - 4 q^{6} + 2 q^{7} + q^{9} + 2 q^{10} + 6 q^{12} + 13 q^{13} + 8 q^{15} + 9 q^{16} + 8 q^{19} + 2 q^{21} + 8 q^{22} + 2 q^{24} - q^{25} + 6 q^{27} + 2 q^{28} + 8 q^{30} + 10 q^{31} + 2 q^{33} + 5 q^{36} - 12 q^{37} - 8 q^{39} + 2 q^{40} - 11 q^{43} - 11 q^{48} + 2 q^{49} - 5 q^{52} - 2 q^{54} - 4 q^{55} - 11 q^{57} + 4 q^{58} - 5 q^{61} - 12 q^{63} - 24 q^{64} + 7 q^{67} + 9 q^{73} + 6 q^{75} + 3 q^{76} + 8 q^{78} + 11 q^{79} - 3 q^{81} + 2 q^{82} + 2 q^{84} - 16 q^{85} - 4 q^{87} - 4 q^{88} + 4 q^{90} + 4 q^{91} + 9 q^{93} - 8 q^{94} + 10 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2793))\)

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
2793.1.b \(\chi_{2793}(932, \cdot)\) None 0 1
2793.1.e \(\chi_{2793}(1177, \cdot)\) None 0 1
2793.1.g \(\chi_{2793}(685, \cdot)\) None 0 1
2793.1.h \(\chi_{2793}(2792, \cdot)\) None 0 1
2793.1.n \(\chi_{2793}(410, \cdot)\) 2793.1.n.a 2 2
2793.1.n.b 2
2793.1.n.c 4
2793.1.o \(\chi_{2793}(373, \cdot)\) None 0 2
2793.1.q \(\chi_{2793}(293, \cdot)\) None 0 2
2793.1.r \(\chi_{2793}(962, \cdot)\) 2793.1.r.a 2 2
2793.1.r.b 2
2793.1.s \(\chi_{2793}(227, \cdot)\) 2793.1.s.a 2 2
2793.1.s.b 2
2793.1.s.c 4
2793.1.s.d 4
2793.1.u \(\chi_{2793}(913, \cdot)\) None 0 2
2793.1.v \(\chi_{2793}(178, \cdot)\) None 0 2
2793.1.y \(\chi_{2793}(391, \cdot)\) None 0 2
2793.1.ba \(\chi_{2793}(949, \cdot)\) None 0 2
2793.1.bb \(\chi_{2793}(1684, \cdot)\) None 0 2
2793.1.be \(\chi_{2793}(1471, \cdot)\) None 0 2
2793.1.bf \(\chi_{2793}(197, \cdot)\) 2793.1.bf.a 2 2
2793.1.bf.b 4
2793.1.bf.c 4
2793.1.bi \(\chi_{2793}(1892, \cdot)\) 2793.1.bi.a 2 2
2793.1.bi.b 2
2793.1.bi.c 4
2793.1.bj \(\chi_{2793}(704, \cdot)\) None 0 2
2793.1.bl \(\chi_{2793}(619, \cdot)\) None 0 2
2793.1.bn \(\chi_{2793}(521, \cdot)\) 2793.1.bn.a 2 2
2793.1.bn.b 2
2793.1.bs \(\chi_{2793}(398, \cdot)\) 2793.1.bs.a 6 6
2793.1.bs.b 6
2793.1.bt \(\chi_{2793}(286, \cdot)\) None 0 6
2793.1.bv \(\chi_{2793}(379, \cdot)\) None 0 6
2793.1.by \(\chi_{2793}(134, \cdot)\) None 0 6
2793.1.ca \(\chi_{2793}(374, \cdot)\) 2793.1.ca.a 6 6
2793.1.cb \(\chi_{2793}(313, \cdot)\) None 0 6
2793.1.cc \(\chi_{2793}(244, \cdot)\) None 0 6
2793.1.cf \(\chi_{2793}(146, \cdot)\) 2793.1.cf.a 6 6
2793.1.cf.b 6
2793.1.cg \(\chi_{2793}(509, \cdot)\) 2793.1.cg.a 6 6
2793.1.ch \(\chi_{2793}(766, \cdot)\) None 0 6
2793.1.ci \(\chi_{2793}(557, \cdot)\) 2793.1.ci.a 6 6
2793.1.cm \(\chi_{2793}(508, \cdot)\) None 0 6
2793.1.cn \(\chi_{2793}(148, \cdot)\) None 0 6
2793.1.co \(\chi_{2793}(491, \cdot)\) 2793.1.co.a 6 6
2793.1.co.b 6
2793.1.cp \(\chi_{2793}(263, \cdot)\) 2793.1.cp.a 6 6
2793.1.ct \(\chi_{2793}(67, \cdot)\) None 0 6
2793.1.cy \(\chi_{2793}(122, \cdot)\) None 0 12
2793.1.da \(\chi_{2793}(220, \cdot)\) None 0 12
2793.1.dc \(\chi_{2793}(191, \cdot)\) None 0 12
2793.1.dd \(\chi_{2793}(296, \cdot)\) None 0 12
2793.1.dg \(\chi_{2793}(239, \cdot)\) 2793.1.dg.a 12 12
2793.1.dg.b 12
2793.1.dh \(\chi_{2793}(274, \cdot)\) None 0 12
2793.1.dk \(\chi_{2793}(88, \cdot)\) None 0 12
2793.1.dl \(\chi_{2793}(37, \cdot)\) None 0 12
2793.1.dn \(\chi_{2793}(349, \cdot)\) None 0 12
2793.1.dq \(\chi_{2793}(334, \cdot)\) None 0 12
2793.1.dr \(\chi_{2793}(115, \cdot)\) None 0 12
2793.1.dt \(\chi_{2793}(341, \cdot)\) None 0 12
2793.1.du \(\chi_{2793}(164, \cdot)\) None 0 12
2793.1.dv \(\chi_{2793}(335, \cdot)\) 2793.1.dv.a 12 12
2793.1.dv.b 12
2793.1.dx \(\chi_{2793}(46, \cdot)\) None 0 12
2793.1.dy \(\chi_{2793}(11, \cdot)\) None 0 12
2793.1.ed \(\chi_{2793}(268, \cdot)\) None 0 36
2793.1.eh \(\chi_{2793}(92, \cdot)\) None 0 36
2793.1.ei \(\chi_{2793}(23, \cdot)\) 2793.1.ei.a 36 36
2793.1.ej \(\chi_{2793}(109, \cdot)\) None 0 36
2793.1.ek \(\chi_{2793}(22, \cdot)\) None 0 36
2793.1.eo \(\chi_{2793}(137, \cdot)\) 2793.1.eo.a 36 36
2793.1.ep \(\chi_{2793}(187, \cdot)\) None 0 36
2793.1.eq \(\chi_{2793}(41, \cdot)\) None 0 36
2793.1.er \(\chi_{2793}(59, \cdot)\) 2793.1.er.a 36 36
2793.1.eu \(\chi_{2793}(61, \cdot)\) None 0 36
2793.1.ev \(\chi_{2793}(55, \cdot)\) None 0 36
2793.1.ew \(\chi_{2793}(143, \cdot)\) 2793.1.ew.a 36 36

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2793))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2793)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(399))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(931))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2793))\)\(^{\oplus 1}\)