Properties

Label 1260.1
Level 1260
Weight 1
Dimension 86
Nonzero newspaces 11
Newform subspaces 27
Sturm bound 82944
Trace bound 16

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Defining parameters

Level: \( N \) = \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 11 \)
Newform subspaces: \( 27 \)
Sturm bound: \(82944\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1260))\).

Total New Old
Modular forms 2106 358 1748
Cusp forms 186 86 100
Eisenstein series 1920 272 1648

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 62 0 24 0

Trace form

\( 86 q - 4 q^{2} + 2 q^{4} + 6 q^{5} - 8 q^{6} + 8 q^{8} + O(q^{10}) \) \( 86 q - 4 q^{2} + 2 q^{4} + 6 q^{5} - 8 q^{6} + 8 q^{8} - 18 q^{14} + 2 q^{15} - 14 q^{16} - 4 q^{18} + 4 q^{19} - 12 q^{20} + 14 q^{21} - 12 q^{22} - 8 q^{24} + 8 q^{25} + 6 q^{29} - 4 q^{31} - 4 q^{32} + 6 q^{35} - 8 q^{36} + 8 q^{37} + 10 q^{39} + 4 q^{42} - 8 q^{45} + 10 q^{46} - 2 q^{49} + 4 q^{50} - 2 q^{51} + 16 q^{53} + 4 q^{54} + 16 q^{57} - 8 q^{60} - 2 q^{61} - 4 q^{64} - 16 q^{69} - 8 q^{70} - 12 q^{71} - 8 q^{72} - 8 q^{78} - 8 q^{79} - 6 q^{80} - 28 q^{81} - 2 q^{84} - 12 q^{85} - 14 q^{86} - 4 q^{88} - 6 q^{89} - 2 q^{91} - 8 q^{94} - 8 q^{96} - 8 q^{98} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1260))\)

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
1260.1.b \(\chi_{1260}(379, \cdot)\) None 0 1
1260.1.e \(\chi_{1260}(449, \cdot)\) None 0 1
1260.1.g \(\chi_{1260}(701, \cdot)\) None 0 1
1260.1.h \(\chi_{1260}(631, \cdot)\) None 0 1
1260.1.j \(\chi_{1260}(181, \cdot)\) None 0 1
1260.1.m \(\chi_{1260}(251, \cdot)\) None 0 1
1260.1.o \(\chi_{1260}(1259, \cdot)\) None 0 1
1260.1.p \(\chi_{1260}(1189, \cdot)\) 1260.1.p.a 1 1
1260.1.p.b 1
1260.1.u \(\chi_{1260}(307, \cdot)\) 1260.1.u.a 4 2
1260.1.u.b 4
1260.1.x \(\chi_{1260}(377, \cdot)\) None 0 2
1260.1.y \(\chi_{1260}(253, \cdot)\) None 0 2
1260.1.bb \(\chi_{1260}(323, \cdot)\) None 0 2
1260.1.bd \(\chi_{1260}(331, \cdot)\) None 0 2
1260.1.be \(\chi_{1260}(221, \cdot)\) None 0 2
1260.1.bg \(\chi_{1260}(569, \cdot)\) None 0 2
1260.1.bj \(\chi_{1260}(79, \cdot)\) 1260.1.bj.a 2 2
1260.1.bj.b 2
1260.1.bj.c 2
1260.1.bj.d 2
1260.1.bk \(\chi_{1260}(971, \cdot)\) None 0 2
1260.1.bn \(\chi_{1260}(901, \cdot)\) None 0 2
1260.1.bp \(\chi_{1260}(419, \cdot)\) 1260.1.bp.a 4 2
1260.1.bp.b 4
1260.1.bq \(\chi_{1260}(229, \cdot)\) None 0 2
1260.1.br \(\chi_{1260}(479, \cdot)\) 1260.1.br.a 4 2
1260.1.br.b 4
1260.1.bt \(\chi_{1260}(349, \cdot)\) 1260.1.bt.a 2 2
1260.1.bt.b 2
1260.1.bt.c 2
1260.1.bt.d 2
1260.1.bu \(\chi_{1260}(601, \cdot)\) None 0 2
1260.1.bw \(\chi_{1260}(131, \cdot)\) None 0 2
1260.1.bz \(\chi_{1260}(241, \cdot)\) None 0 2
1260.1.cb \(\chi_{1260}(671, \cdot)\) None 0 2
1260.1.cc \(\chi_{1260}(649, \cdot)\) None 0 2
1260.1.cd \(\chi_{1260}(719, \cdot)\) None 0 2
1260.1.cf \(\chi_{1260}(809, \cdot)\) 1260.1.cf.a 8 2
1260.1.ci \(\chi_{1260}(739, \cdot)\) 1260.1.ci.a 2 2
1260.1.ci.b 2
1260.1.ck \(\chi_{1260}(281, \cdot)\) None 0 2
1260.1.cm \(\chi_{1260}(151, \cdot)\) None 0 2
1260.1.cn \(\chi_{1260}(401, \cdot)\) None 0 2
1260.1.cp \(\chi_{1260}(211, \cdot)\) None 0 2
1260.1.cr \(\chi_{1260}(799, \cdot)\) None 0 2
1260.1.ct \(\chi_{1260}(149, \cdot)\) None 0 2
1260.1.cw \(\chi_{1260}(499, \cdot)\) 1260.1.cw.a 2 2
1260.1.cw.b 2
1260.1.cw.c 2
1260.1.cw.d 2
1260.1.cy \(\chi_{1260}(29, \cdot)\) None 0 2
1260.1.da \(\chi_{1260}(991, \cdot)\) None 0 2
1260.1.db \(\chi_{1260}(1061, \cdot)\) None 0 2
1260.1.dd \(\chi_{1260}(409, \cdot)\) None 0 2
1260.1.de \(\chi_{1260}(59, \cdot)\) 1260.1.de.a 4 2
1260.1.de.b 4
1260.1.dg \(\chi_{1260}(311, \cdot)\) None 0 2
1260.1.dj \(\chi_{1260}(61, \cdot)\) None 0 2
1260.1.dk \(\chi_{1260}(173, \cdot)\) None 0 4
1260.1.dn \(\chi_{1260}(187, \cdot)\) None 0 4
1260.1.dp \(\chi_{1260}(337, \cdot)\) None 0 4
1260.1.dr \(\chi_{1260}(23, \cdot)\) None 0 4
1260.1.dt \(\chi_{1260}(107, \cdot)\) None 0 4
1260.1.du \(\chi_{1260}(37, \cdot)\) None 0 4
1260.1.dw \(\chi_{1260}(277, \cdot)\) None 0 4
1260.1.dy \(\chi_{1260}(407, \cdot)\) None 0 4
1260.1.eb \(\chi_{1260}(223, \cdot)\) 1260.1.eb.a 8 4
1260.1.eb.b 8
1260.1.ed \(\chi_{1260}(257, \cdot)\) None 0 4
1260.1.ef \(\chi_{1260}(17, \cdot)\) None 0 4
1260.1.eg \(\chi_{1260}(523, \cdot)\) None 0 4
1260.1.ei \(\chi_{1260}(103, \cdot)\) None 0 4
1260.1.ek \(\chi_{1260}(293, \cdot)\) None 0 4
1260.1.em \(\chi_{1260}(347, \cdot)\) None 0 4
1260.1.ep \(\chi_{1260}(193, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1260))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1260)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 2}\)