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Properties

Label 3216.1
Level 3216
Weight 1
Dimension 106
Nonzero newspaces 7
Newform subspaces 14
Sturm bound 574464
Trace bound 3

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Defining parameters

Level: \( N \) = \( 3216 = 2^{4} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 14 \)
Sturm bound: \(574464\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3216))\).

Total New Old
Modular forms 4250 690 3560
Cusp forms 554 106 448
Eisenstein series 3696 584 3112

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 102 4 0 0

Trace form

\( 106 q + q^{3} + 4 q^{7} - q^{9} - 4 q^{13} - 6 q^{21} + 11 q^{25} + q^{27} - 2 q^{33} + 2 q^{39} + 2 q^{43} - 3 q^{49} + 2 q^{51} - 2 q^{57} - 4 q^{61} + 5 q^{67} + 2 q^{69} - 4 q^{73} + q^{75} + 4 q^{79}+ \cdots - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3216))\)

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
3216.1.b \(\chi_{3216}(2545, \cdot)\) None 0 1
3216.1.d \(\chi_{3216}(1207, \cdot)\) None 0 1
3216.1.g \(\chi_{3216}(1073, \cdot)\) None 0 1
3216.1.i \(\chi_{3216}(1607, \cdot)\) None 0 1
3216.1.k \(\chi_{3216}(2815, \cdot)\) None 0 1
3216.1.m \(\chi_{3216}(937, \cdot)\) None 0 1
3216.1.n \(\chi_{3216}(3215, \cdot)\) 3216.1.n.a 1 1
3216.1.n.b 1
3216.1.n.c 2
3216.1.n.d 2
3216.1.p \(\chi_{3216}(2681, \cdot)\) None 0 1
3216.1.r \(\chi_{3216}(803, \cdot)\) None 0 2
3216.1.s \(\chi_{3216}(269, \cdot)\) None 0 2
3216.1.x \(\chi_{3216}(133, \cdot)\) None 0 2
3216.1.y \(\chi_{3216}(403, \cdot)\) None 0 2
3216.1.z \(\chi_{3216}(1847, \cdot)\) None 0 2
3216.1.bb \(\chi_{3216}(305, \cdot)\) 3216.1.bb.a 2 2
3216.1.bb.b 4
3216.1.be \(\chi_{3216}(439, \cdot)\) None 0 2
3216.1.bg \(\chi_{3216}(97, \cdot)\) None 0 2
3216.1.bh \(\chi_{3216}(1913, \cdot)\) None 0 2
3216.1.bj \(\chi_{3216}(239, \cdot)\) 3216.1.bj.a 2 2
3216.1.bj.b 2
3216.1.bk \(\chi_{3216}(1177, \cdot)\) None 0 2
3216.1.bm \(\chi_{3216}(2047, \cdot)\) None 0 2
3216.1.bp \(\chi_{3216}(163, \cdot)\) None 0 4
3216.1.bq \(\chi_{3216}(373, \cdot)\) None 0 4
3216.1.bv \(\chi_{3216}(29, \cdot)\) None 0 4
3216.1.bw \(\chi_{3216}(1043, \cdot)\) None 0 4
3216.1.bx \(\chi_{3216}(89, \cdot)\) None 0 10
3216.1.bz \(\chi_{3216}(527, \cdot)\) 3216.1.bz.a 10 10
3216.1.bz.b 10
3216.1.ca \(\chi_{3216}(313, \cdot)\) None 0 10
3216.1.cc \(\chi_{3216}(223, \cdot)\) None 0 10
3216.1.ce \(\chi_{3216}(119, \cdot)\) None 0 10
3216.1.cg \(\chi_{3216}(545, \cdot)\) 3216.1.cg.a 10 10
3216.1.cj \(\chi_{3216}(679, \cdot)\) None 0 10
3216.1.cl \(\chi_{3216}(673, \cdot)\) None 0 10
3216.1.cn \(\chi_{3216}(91, \cdot)\) None 0 20
3216.1.co \(\chi_{3216}(109, \cdot)\) None 0 20
3216.1.ct \(\chi_{3216}(149, \cdot)\) None 0 20
3216.1.cu \(\chi_{3216}(179, \cdot)\) None 0 20
3216.1.cw \(\chi_{3216}(127, \cdot)\) None 0 20
3216.1.cy \(\chi_{3216}(409, \cdot)\) None 0 20
3216.1.cz \(\chi_{3216}(95, \cdot)\) 3216.1.cz.a 20 20
3216.1.cz.b 20
3216.1.db \(\chi_{3216}(425, \cdot)\) None 0 20
3216.1.dc \(\chi_{3216}(145, \cdot)\) None 0 20
3216.1.de \(\chi_{3216}(55, \cdot)\) None 0 20
3216.1.dh \(\chi_{3216}(17, \cdot)\) 3216.1.dh.a 20 20
3216.1.dj \(\chi_{3216}(503, \cdot)\) None 0 20
3216.1.dk \(\chi_{3216}(11, \cdot)\) None 0 40
3216.1.dl \(\chi_{3216}(77, \cdot)\) None 0 40
3216.1.dq \(\chi_{3216}(13, \cdot)\) None 0 40
3216.1.dr \(\chi_{3216}(19, \cdot)\) None 0 40

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3216))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3216)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(201))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(268))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(402))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(536))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(804))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1072))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1608))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3216))\)\(^{\oplus 1}\)