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Properties

Label 3780.1
Level 3780
Weight 1
Dimension 264
Nonzero newspaces 17
Newform subspaces 54
Sturm bound 746496
Trace bound 45

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Defining parameters

Level: \( N \) = \( 3780 = 2^{2} \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 17 \)
Newform subspaces: \( 54 \)
Sturm bound: \(746496\)
Trace bound: \(45\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3780))\).

Total New Old
Modular forms 8008 1224 6784
Cusp forms 808 264 544
Eisenstein series 7200 960 6240

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 232 0 32 0

Trace form

\( 264 q + 4 q^{2} + 8 q^{4} - 4 q^{5} + 12 q^{6} - 8 q^{8} + 6 q^{9} + O(q^{10}) \) \( 264 q + 4 q^{2} + 8 q^{4} - 4 q^{5} + 12 q^{6} - 8 q^{8} + 6 q^{9} - 4 q^{10} + 8 q^{11} + 16 q^{13} + 20 q^{14} + 8 q^{20} + 4 q^{22} + 12 q^{29} + 4 q^{32} - 8 q^{34} - 20 q^{35} + 12 q^{36} - 8 q^{37} - 12 q^{39} - 4 q^{40} - 20 q^{41} + 12 q^{45} + 16 q^{46} + 4 q^{49} - 4 q^{50} + 8 q^{52} - 16 q^{53} + 8 q^{56} + 16 q^{61} - 4 q^{64} - 10 q^{65} - 24 q^{69} - 6 q^{70} + 8 q^{71} + 8 q^{73} - 14 q^{79} - 16 q^{80} + 6 q^{81} - 12 q^{84} - 38 q^{85} + 12 q^{86} + 12 q^{88} + 4 q^{89} + 4 q^{91} - 28 q^{94} + 8 q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3780))\)

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
3780.1.b \(\chi_{3780}(379, \cdot)\) None 0 1
3780.1.e \(\chi_{3780}(2969, \cdot)\) None 0 1
3780.1.g \(\chi_{3780}(701, \cdot)\) None 0 1
3780.1.h \(\chi_{3780}(1891, \cdot)\) None 0 1
3780.1.j \(\chi_{3780}(2701, \cdot)\) None 0 1
3780.1.m \(\chi_{3780}(1511, \cdot)\) None 0 1
3780.1.o \(\chi_{3780}(3779, \cdot)\) 3780.1.o.a 1 1
3780.1.o.b 1
3780.1.o.c 1
3780.1.o.d 1
3780.1.o.e 1
3780.1.o.f 1
3780.1.o.g 1
3780.1.o.h 1
3780.1.o.i 4
3780.1.o.j 4
3780.1.p \(\chi_{3780}(1189, \cdot)\) None 0 1
3780.1.u \(\chi_{3780}(1567, \cdot)\) 3780.1.u.a 8 2
3780.1.u.b 8
3780.1.x \(\chi_{3780}(377, \cdot)\) None 0 2
3780.1.y \(\chi_{3780}(757, \cdot)\) None 0 2
3780.1.bb \(\chi_{3780}(323, \cdot)\) None 0 2
3780.1.bd \(\chi_{3780}(2251, \cdot)\) None 0 2
3780.1.be \(\chi_{3780}(3581, \cdot)\) None 0 2
3780.1.bg \(\chi_{3780}(2069, \cdot)\) None 0 2
3780.1.bj \(\chi_{3780}(739, \cdot)\) 3780.1.bj.a 2 2
3780.1.bj.b 2
3780.1.bj.c 2
3780.1.bj.d 2
3780.1.bk \(\chi_{3780}(971, \cdot)\) None 0 2
3780.1.bn \(\chi_{3780}(1081, \cdot)\) None 0 2
3780.1.bp \(\chi_{3780}(1259, \cdot)\) 3780.1.bp.a 4 2
3780.1.bp.b 4
3780.1.bq \(\chi_{3780}(829, \cdot)\) None 0 2
3780.1.br \(\chi_{3780}(719, \cdot)\) 3780.1.br.a 4 2
3780.1.br.b 4
3780.1.bt \(\chi_{3780}(2449, \cdot)\) 3780.1.bt.a 2 2
3780.1.bt.b 2
3780.1.bt.c 2
3780.1.bt.d 2
3780.1.bu \(\chi_{3780}(181, \cdot)\) None 0 2
3780.1.bw \(\chi_{3780}(2231, \cdot)\) None 0 2
3780.1.bz \(\chi_{3780}(901, \cdot)\) None 0 2
3780.1.cb \(\chi_{3780}(251, \cdot)\) None 0 2
3780.1.cc \(\chi_{3780}(649, \cdot)\) None 0 2
3780.1.cd \(\chi_{3780}(2159, \cdot)\) None 0 2
3780.1.cf \(\chi_{3780}(809, \cdot)\) None 0 2
3780.1.ci \(\chi_{3780}(919, \cdot)\) 3780.1.ci.a 4 2
3780.1.ci.b 4
3780.1.ck \(\chi_{3780}(1961, \cdot)\) None 0 2
3780.1.cm \(\chi_{3780}(991, \cdot)\) None 0 2
3780.1.cn \(\chi_{3780}(1061, \cdot)\) None 0 2
3780.1.cp \(\chi_{3780}(631, \cdot)\) None 0 2
3780.1.cr \(\chi_{3780}(1639, \cdot)\) None 0 2
3780.1.ct \(\chi_{3780}(989, \cdot)\) None 0 2
3780.1.cw \(\chi_{3780}(3259, \cdot)\) 3780.1.cw.a 2 2
3780.1.cw.b 2
3780.1.cw.c 2
3780.1.cw.d 2
3780.1.cy \(\chi_{3780}(449, \cdot)\) None 0 2
3780.1.da \(\chi_{3780}(2431, \cdot)\) None 0 2
3780.1.db \(\chi_{3780}(1241, \cdot)\) None 0 2
3780.1.dd \(\chi_{3780}(1909, \cdot)\) None 0 2
3780.1.de \(\chi_{3780}(1979, \cdot)\) 3780.1.de.a 4 2
3780.1.de.b 4
3780.1.dg \(\chi_{3780}(1151, \cdot)\) None 0 2
3780.1.dj \(\chi_{3780}(3421, \cdot)\) None 0 2
3780.1.dn \(\chi_{3780}(17, \cdot)\) None 0 4
3780.1.dq \(\chi_{3780}(2287, \cdot)\) None 0 4
3780.1.ds \(\chi_{3780}(253, \cdot)\) None 0 4
3780.1.du \(\chi_{3780}(683, \cdot)\) None 0 4
3780.1.dw \(\chi_{3780}(107, \cdot)\) 3780.1.dw.a 8 4
3780.1.dw.b 8
3780.1.dx \(\chi_{3780}(1297, \cdot)\) None 0 4
3780.1.dz \(\chi_{3780}(37, \cdot)\) None 0 4
3780.1.eb \(\chi_{3780}(827, \cdot)\) None 0 4
3780.1.ee \(\chi_{3780}(307, \cdot)\) 3780.1.ee.a 8 4
3780.1.ee.b 8
3780.1.eg \(\chi_{3780}(1097, \cdot)\) None 0 4
3780.1.ei \(\chi_{3780}(593, \cdot)\) None 0 4
3780.1.ej \(\chi_{3780}(703, \cdot)\) None 0 4
3780.1.el \(\chi_{3780}(523, \cdot)\) None 0 4
3780.1.en \(\chi_{3780}(1637, \cdot)\) None 0 4
3780.1.ep \(\chi_{3780}(2447, \cdot)\) None 0 4
3780.1.es \(\chi_{3780}(1117, \cdot)\) None 0 4
3780.1.et \(\chi_{3780}(241, \cdot)\) None 0 6
3780.1.ew \(\chi_{3780}(499, \cdot)\) 3780.1.ew.a 6 6
3780.1.ew.b 6
3780.1.ew.c 6
3780.1.ew.d 6
3780.1.ey \(\chi_{3780}(401, \cdot)\) None 0 6
3780.1.ez \(\chi_{3780}(479, \cdot)\) 3780.1.ez.a 12 6
3780.1.ez.b 12
3780.1.fb \(\chi_{3780}(569, \cdot)\) None 0 6
3780.1.fd \(\chi_{3780}(671, \cdot)\) None 0 6
3780.1.ff \(\chi_{3780}(29, \cdot)\) None 0 6
3780.1.fg \(\chi_{3780}(311, \cdot)\) None 0 6
3780.1.fi \(\chi_{3780}(409, \cdot)\) None 0 6
3780.1.fk \(\chi_{3780}(211, \cdot)\) None 0 6
3780.1.fl \(\chi_{3780}(349, \cdot)\) 3780.1.fl.a 6 6
3780.1.fl.b 6
3780.1.fl.c 6
3780.1.fl.d 6
3780.1.fn \(\chi_{3780}(331, \cdot)\) None 0 6
3780.1.fp \(\chi_{3780}(59, \cdot)\) 3780.1.fp.a 12 6
3780.1.fp.b 12
3780.1.fr \(\chi_{3780}(281, \cdot)\) None 0 6
3780.1.fu \(\chi_{3780}(419, \cdot)\) 3780.1.fu.a 12 6
3780.1.fu.b 12
3780.1.fw \(\chi_{3780}(221, \cdot)\) None 0 6
3780.1.fy \(\chi_{3780}(79, \cdot)\) 3780.1.fy.a 6 6
3780.1.fy.b 6
3780.1.fy.c 6
3780.1.fy.d 6
3780.1.ga \(\chi_{3780}(601, \cdot)\) None 0 6
3780.1.gb \(\chi_{3780}(799, \cdot)\) None 0 6
3780.1.gd \(\chi_{3780}(61, \cdot)\) None 0 6
3780.1.gf \(\chi_{3780}(151, \cdot)\) None 0 6
3780.1.gi \(\chi_{3780}(229, \cdot)\) None 0 6
3780.1.gj \(\chi_{3780}(131, \cdot)\) None 0 6
3780.1.gk \(\chi_{3780}(149, \cdot)\) None 0 6
3780.1.gm \(\chi_{3780}(277, \cdot)\) None 0 12
3780.1.gp \(\chi_{3780}(103, \cdot)\) None 0 12
3780.1.gq \(\chi_{3780}(407, \cdot)\) None 0 12
3780.1.gs \(\chi_{3780}(347, \cdot)\) None 0 12
3780.1.gv \(\chi_{3780}(293, \cdot)\) None 0 12
3780.1.gx \(\chi_{3780}(173, \cdot)\) None 0 12
3780.1.gy \(\chi_{3780}(337, \cdot)\) None 0 12
3780.1.ha \(\chi_{3780}(193, \cdot)\) None 0 12
3780.1.hd \(\chi_{3780}(223, \cdot)\) None 0 12
3780.1.hf \(\chi_{3780}(187, \cdot)\) None 0 12
3780.1.hg \(\chi_{3780}(23, \cdot)\) None 0 12
3780.1.hj \(\chi_{3780}(257, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3780))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3780)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 48}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 36}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(756))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(945))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1260))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1890))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3780))\)\(^{\oplus 1}\)