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Properties

Label 3072.1
Level 3072
Weight 1
Dimension 64
Nonzero newspaces 4
Newform subspaces 15
Sturm bound 524288
Trace bound 9

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Defining parameters

Level: \( N \) = \( 3072 = 2^{10} \cdot 3 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 15 \)
Sturm bound: \(524288\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3072))\).

Total New Old
Modular forms 3544 544 3000
Cusp forms 216 64 152
Eisenstein series 3328 480 2848

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 64 0 0 0

Trace form

\( 64 q + O(q^{10}) \) \( 64 q + 16 q^{49} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3072))\)

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
3072.1.b \(\chi_{3072}(511, \cdot)\) None 0 1
3072.1.e \(\chi_{3072}(1025, \cdot)\) 3072.1.e.a 2 1
3072.1.e.b 2
3072.1.g \(\chi_{3072}(2047, \cdot)\) None 0 1
3072.1.h \(\chi_{3072}(2561, \cdot)\) 3072.1.h.a 4 1
3072.1.i \(\chi_{3072}(257, \cdot)\) 3072.1.i.a 2 2
3072.1.i.b 2
3072.1.i.c 2
3072.1.i.d 2
3072.1.i.e 4
3072.1.i.f 4
3072.1.i.g 4
3072.1.i.h 4
3072.1.l \(\chi_{3072}(1279, \cdot)\) None 0 2
3072.1.m \(\chi_{3072}(127, \cdot)\) None 0 4
3072.1.p \(\chi_{3072}(641, \cdot)\) 3072.1.p.a 8 4
3072.1.p.b 8
3072.1.p.c 8
3072.1.p.d 8
3072.1.q \(\chi_{3072}(65, \cdot)\) None 0 8
3072.1.t \(\chi_{3072}(319, \cdot)\) None 0 8
3072.1.u \(\chi_{3072}(31, \cdot)\) None 0 16
3072.1.x \(\chi_{3072}(161, \cdot)\) None 0 16
3072.1.y \(\chi_{3072}(17, \cdot)\) None 0 32
3072.1.bb \(\chi_{3072}(79, \cdot)\) None 0 32
3072.1.bc \(\chi_{3072}(7, \cdot)\) None 0 64
3072.1.bf \(\chi_{3072}(41, \cdot)\) None 0 64
3072.1.bg \(\chi_{3072}(5, \cdot)\) None 0 128
3072.1.bj \(\chi_{3072}(19, \cdot)\) None 0 128

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3072))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3072)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 22}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 11}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 14}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(768))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1024))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1536))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3072))\)\(^{\oplus 1}\)