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Properties

Label 3776.1
Level 3776
Weight 1
Dimension 90
Nonzero newspaces 4
Newform subspaces 11
Sturm bound 890880
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3776 = 2^{6} \cdot 59 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 11 \)
Sturm bound: \(890880\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3776))\).

Total New Old
Modular forms 4500 1344 3156
Cusp forms 324 90 234
Eisenstein series 4176 1254 2922

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 82 0 8 0

Trace form

\( 90 q + 2 q^{5} - 6 q^{9} + O(q^{10}) \) \( 90 q + 2 q^{5} - 6 q^{9} + 6 q^{17} - 4 q^{19} + 8 q^{21} - 14 q^{25} - 2 q^{29} - 4 q^{35} - 2 q^{41} + 10 q^{45} + 26 q^{49} - 2 q^{53} + 8 q^{57} + 4 q^{63} - 4 q^{79} + 4 q^{81} + 8 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3776))\)

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
3776.1.c \(\chi_{3776}(353, \cdot)\) 3776.1.c.a 2 1
3776.1.c.b 4
3776.1.c.c 12
3776.1.d \(\chi_{3776}(1535, \cdot)\) None 0 1
3776.1.g \(\chi_{3776}(3423, \cdot)\) None 0 1
3776.1.h \(\chi_{3776}(2241, \cdot)\) 3776.1.h.a 1 1
3776.1.h.b 1
3776.1.h.c 2
3776.1.h.d 2
3776.1.h.e 3
3776.1.h.f 3
3776.1.j \(\chi_{3776}(1297, \cdot)\) 3776.1.j.a 4 2
3776.1.l \(\chi_{3776}(591, \cdot)\) None 0 2
3776.1.m \(\chi_{3776}(825, \cdot)\) None 0 4
3776.1.o \(\chi_{3776}(119, \cdot)\) None 0 4
3776.1.s \(\chi_{3776}(355, \cdot)\) None 0 8
3776.1.t \(\chi_{3776}(117, \cdot)\) None 0 8
3776.1.v \(\chi_{3776}(65, \cdot)\) None 0 28
3776.1.w \(\chi_{3776}(95, \cdot)\) None 0 28
3776.1.z \(\chi_{3776}(63, \cdot)\) None 0 28
3776.1.ba \(\chi_{3776}(33, \cdot)\) 3776.1.ba.a 56 28
3776.1.bc \(\chi_{3776}(15, \cdot)\) None 0 56
3776.1.be \(\chi_{3776}(113, \cdot)\) None 0 56
3776.1.bh \(\chi_{3776}(7, \cdot)\) None 0 112
3776.1.bj \(\chi_{3776}(73, \cdot)\) None 0 112
3776.1.bk \(\chi_{3776}(13, \cdot)\) None 0 224
3776.1.bl \(\chi_{3776}(3, \cdot)\) None 0 224

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3776))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3776)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(236))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(472))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(944))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1888))\)\(^{\oplus 2}\)