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Properties

Label 3872.1
Level 3872
Weight 1
Dimension 96
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 929280
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3872 = 2^{5} \cdot 11^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(929280\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3872))\).

Total New Old
Modular forms 5622 1501 4121
Cusp forms 502 96 406
Eisenstein series 5120 1405 3715

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 96 0 0 0

Trace form

\( 96 q - 2 q^{3} + 3 q^{9} + O(q^{10}) \) \( 96 q - 2 q^{3} + 3 q^{9} + 2 q^{17} + 8 q^{19} + q^{25} + 6 q^{27} - 5 q^{33} + 2 q^{41} - 2 q^{43} + q^{49} + 6 q^{51} - 6 q^{57} + 8 q^{59} + 8 q^{67} + 2 q^{73} + 8 q^{75} - 5 q^{81} + 8 q^{83} - 8 q^{89} - 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3872))\)

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
3872.1.b \(\chi_{3872}(241, \cdot)\) None 0 1
3872.1.d \(\chi_{3872}(1695, \cdot)\) None 0 1
3872.1.f \(\chi_{3872}(3631, \cdot)\) 3872.1.f.a 2 1
3872.1.f.b 2
3872.1.h \(\chi_{3872}(2177, \cdot)\) 3872.1.h.a 2 1
3872.1.h.b 4
3872.1.k \(\chi_{3872}(727, \cdot)\) None 0 2
3872.1.l \(\chi_{3872}(1209, \cdot)\) None 0 2
3872.1.o \(\chi_{3872}(725, \cdot)\) None 0 4
3872.1.p \(\chi_{3872}(243, \cdot)\) None 0 4
3872.1.r \(\chi_{3872}(161, \cdot)\) 3872.1.r.a 8 4
3872.1.r.b 16
3872.1.t \(\chi_{3872}(1455, \cdot)\) 3872.1.t.a 4 4
3872.1.t.b 4
3872.1.t.c 4
3872.1.v \(\chi_{3872}(511, \cdot)\) None 0 4
3872.1.x \(\chi_{3872}(1201, \cdot)\) None 0 4
3872.1.z \(\chi_{3872}(233, \cdot)\) None 0 8
3872.1.ba \(\chi_{3872}(487, \cdot)\) None 0 8
3872.1.be \(\chi_{3872}(287, \cdot)\) None 0 10
3872.1.bg \(\chi_{3872}(593, \cdot)\) None 0 10
3872.1.bh \(\chi_{3872}(65, \cdot)\) None 0 10
3872.1.bj \(\chi_{3872}(111, \cdot)\) 3872.1.bj.a 10 10
3872.1.bl \(\chi_{3872}(3, \cdot)\) None 0 16
3872.1.bm \(\chi_{3872}(645, \cdot)\) None 0 16
3872.1.bo \(\chi_{3872}(153, \cdot)\) None 0 20
3872.1.bp \(\chi_{3872}(23, \cdot)\) None 0 20
3872.1.bu \(\chi_{3872}(67, \cdot)\) None 0 40
3872.1.bv \(\chi_{3872}(21, \cdot)\) None 0 40
3872.1.bx \(\chi_{3872}(15, \cdot)\) 3872.1.bx.a 40 40
3872.1.bz \(\chi_{3872}(129, \cdot)\) None 0 40
3872.1.ca \(\chi_{3872}(17, \cdot)\) None 0 40
3872.1.cc \(\chi_{3872}(31, \cdot)\) None 0 40
3872.1.cg \(\chi_{3872}(71, \cdot)\) None 0 80
3872.1.ch \(\chi_{3872}(41, \cdot)\) None 0 80
3872.1.cj \(\chi_{3872}(13, \cdot)\) None 0 160
3872.1.ck \(\chi_{3872}(59, \cdot)\) None 0 160

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3872))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3872)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1936))\)\(^{\oplus 2}\)