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Properties

Label 3672.1
Level 3672
Weight 1
Dimension 260
Nonzero newspaces 12
Newform subspaces 24
Sturm bound 746496
Trace bound 13

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Defining parameters

Level: \( N \) = \( 3672 = 2^{3} \cdot 3^{3} \cdot 17 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 24 \)
Sturm bound: \(746496\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3672))\).

Total New Old
Modular forms 6586 1220 5366
Cusp forms 826 260 566
Eisenstein series 5760 960 4800

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 244 0 16 0

Trace form

\( 260 q - 2 q^{2} + 6 q^{4} + 8 q^{7} + 10 q^{8} + O(q^{10}) \) \( 260 q - 2 q^{2} + 6 q^{4} + 8 q^{7} + 10 q^{8} - 4 q^{10} + 8 q^{11} + 6 q^{12} - 2 q^{16} - 2 q^{17} - 12 q^{18} + 8 q^{19} + 4 q^{22} + 2 q^{25} + 6 q^{27} + 4 q^{31} - 2 q^{32} + 6 q^{33} - 2 q^{34} + 6 q^{38} - 4 q^{40} + 8 q^{41} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 6 q^{49} + 14 q^{50} - 6 q^{51} - 8 q^{52} + 6 q^{57} + 4 q^{58} - 10 q^{59} + 4 q^{61} + 6 q^{64} + 4 q^{67} - 5 q^{68} - 14 q^{76} + 8 q^{79} + 8 q^{82} + 12 q^{83} + 8 q^{86} - 14 q^{88} + 2 q^{89} - 12 q^{96} + 8 q^{97} + 10 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3672))\)

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
3672.1.b \(\chi_{3672}(917, \cdot)\) 3672.1.b.a 1 1
3672.1.b.b 1
3672.1.b.c 1
3672.1.b.d 1
3672.1.d \(\chi_{3672}(2755, \cdot)\) None 0 1
3672.1.g \(\chi_{3672}(3401, \cdot)\) None 0 1
3672.1.i \(\chi_{3672}(271, \cdot)\) None 0 1
3672.1.k \(\chi_{3672}(919, \cdot)\) None 0 1
3672.1.m \(\chi_{3672}(2753, \cdot)\) 3672.1.m.a 4 1
3672.1.n \(\chi_{3672}(2107, \cdot)\) None 0 1
3672.1.p \(\chi_{3672}(1565, \cdot)\) None 0 1
3672.1.s \(\chi_{3672}(1891, \cdot)\) None 0 2
3672.1.u \(\chi_{3672}(701, \cdot)\) 3672.1.u.a 4 2
3672.1.u.b 4
3672.1.v \(\chi_{3672}(2537, \cdot)\) 3672.1.v.a 4 2
3672.1.x \(\chi_{3672}(55, \cdot)\) None 0 2
3672.1.z \(\chi_{3672}(341, \cdot)\) None 0 2
3672.1.bb \(\chi_{3672}(883, \cdot)\) 3672.1.bb.a 2 2
3672.1.bb.b 2
3672.1.bc \(\chi_{3672}(305, \cdot)\) None 0 2
3672.1.be \(\chi_{3672}(2143, \cdot)\) None 0 2
3672.1.bg \(\chi_{3672}(1495, \cdot)\) None 0 2
3672.1.bi \(\chi_{3672}(953, \cdot)\) None 0 2
3672.1.bl \(\chi_{3672}(307, \cdot)\) None 0 2
3672.1.bn \(\chi_{3672}(2141, \cdot)\) None 0 2
3672.1.bo \(\chi_{3672}(161, \cdot)\) None 0 4
3672.1.bp \(\chi_{3672}(1351, \cdot)\) None 0 4
3672.1.bu \(\chi_{3672}(53, \cdot)\) None 0 4
3672.1.bv \(\chi_{3672}(1243, \cdot)\) None 0 4
3672.1.bx \(\chi_{3672}(89, \cdot)\) None 0 4
3672.1.bz \(\chi_{3672}(1279, \cdot)\) None 0 4
3672.1.cc \(\chi_{3672}(523, \cdot)\) 3672.1.cc.a 4 4
3672.1.cc.b 4
3672.1.ce \(\chi_{3672}(557, \cdot)\) None 0 4
3672.1.cf \(\chi_{3672}(107, \cdot)\) None 0 8
3672.1.ci \(\chi_{3672}(109, \cdot)\) None 0 8
3672.1.cj \(\chi_{3672}(649, \cdot)\) None 0 8
3672.1.cm \(\chi_{3672}(215, \cdot)\) None 0 8
3672.1.cn \(\chi_{3672}(67, \cdot)\) 3672.1.cn.a 6 6
3672.1.cn.b 6
3672.1.co \(\chi_{3672}(715, \cdot)\) None 0 6
3672.1.cq \(\chi_{3672}(137, \cdot)\) None 0 6
3672.1.cs \(\chi_{3672}(713, \cdot)\) None 0 6
3672.1.cv \(\chi_{3672}(101, \cdot)\) None 0 6
3672.1.cx \(\chi_{3672}(749, \cdot)\) None 0 6
3672.1.cz \(\chi_{3672}(103, \cdot)\) None 0 6
3672.1.db \(\chi_{3672}(679, \cdot)\) None 0 6
3672.1.de \(\chi_{3672}(773, \cdot)\) None 0 8
3672.1.df \(\chi_{3672}(19, \cdot)\) 3672.1.df.a 8 8
3672.1.df.b 8
3672.1.dg \(\chi_{3672}(665, \cdot)\) None 0 8
3672.1.dh \(\chi_{3672}(127, \cdot)\) None 0 8
3672.1.dk \(\chi_{3672}(149, \cdot)\) None 0 12
3672.1.dm \(\chi_{3672}(319, \cdot)\) None 0 12
3672.1.dp \(\chi_{3672}(115, \cdot)\) 3672.1.dp.a 12 12
3672.1.dp.b 12
3672.1.dr \(\chi_{3672}(353, \cdot)\) None 0 12
3672.1.ds \(\chi_{3672}(37, \cdot)\) None 0 16
3672.1.dv \(\chi_{3672}(683, \cdot)\) 3672.1.dv.a 16 16
3672.1.dv.b 16
3672.1.dw \(\chi_{3672}(71, \cdot)\) None 0 16
3672.1.dz \(\chi_{3672}(73, \cdot)\) None 0 16
3672.1.ea \(\chi_{3672}(77, \cdot)\) None 0 24
3672.1.ed \(\chi_{3672}(43, \cdot)\) 3672.1.ed.a 24 24
3672.1.ed.b 24
3672.1.ee \(\chi_{3672}(185, \cdot)\) None 0 24
3672.1.eh \(\chi_{3672}(151, \cdot)\) None 0 24
3672.1.ej \(\chi_{3672}(97, \cdot)\) None 0 48
3672.1.ek \(\chi_{3672}(23, \cdot)\) None 0 48
3672.1.en \(\chi_{3672}(61, \cdot)\) None 0 48
3672.1.eo \(\chi_{3672}(11, \cdot)\) 3672.1.eo.a 48 48
3672.1.eo.b 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3672))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3672)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(459))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(612))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1836))\)\(^{\oplus 2}\)