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Properties

Label 3844.1
Level 3844
Weight 1
Dimension 191
Nonzero newspaces 4
Newform subspaces 25
Sturm bound 922560
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3844 = 2^{2} \cdot 31^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 25 \)
Sturm bound: \(922560\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3844))\).

Total New Old
Modular forms 3697 1512 2185
Cusp forms 247 191 56
Eisenstein series 3450 1321 2129

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 135 56 0 0

Trace form

\( 191 q + 4 q^{4} + 2 q^{5} + 2 q^{6} + O(q^{10}) \) \( 191 q + 4 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{13} - 2 q^{14} - 4 q^{16} + 2 q^{17} - 2 q^{20} + 2 q^{21} + 2 q^{22} - 2 q^{24} - 4 q^{30} - 30 q^{32} + 4 q^{33} + 2 q^{37} + 2 q^{38} + 2 q^{41} + 2 q^{52} - 2 q^{53} - 4 q^{54} + 2 q^{56} - 2 q^{57} + 4 q^{64} - 2 q^{65} - 2 q^{68} + 4 q^{70} + 2 q^{73} - 4 q^{77} + 4 q^{78} + 2 q^{80} - 2 q^{81} - 2 q^{84} - 4 q^{85} + 2 q^{86} - 2 q^{88} + 2 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3844))\)

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
3844.1.b \(\chi_{3844}(1923, \cdot)\) 3844.1.b.a 1 1
3844.1.b.b 2
3844.1.b.c 2
3844.1.b.d 2
3844.1.b.e 2
3844.1.b.f 4
3844.1.c \(\chi_{3844}(1921, \cdot)\) None 0 1
3844.1.h \(\chi_{3844}(1401, \cdot)\) None 0 2
3844.1.i \(\chi_{3844}(439, \cdot)\) 3844.1.i.a 2 2
3844.1.i.b 2
3844.1.i.c 2
3844.1.i.d 4
3844.1.i.e 4
3844.1.i.f 8
3844.1.k \(\chi_{3844}(333, \cdot)\) None 0 4
3844.1.l \(\chi_{3844}(531, \cdot)\) 3844.1.l.a 4 4
3844.1.l.b 8
3844.1.l.c 8
3844.1.l.d 8
3844.1.l.e 8
3844.1.l.f 16
3844.1.n \(\chi_{3844}(235, \cdot)\) 3844.1.n.a 8 8
3844.1.n.b 8
3844.1.n.c 8
3844.1.n.d 16
3844.1.n.e 16
3844.1.n.f 16
3844.1.n.g 32
3844.1.o \(\chi_{3844}(117, \cdot)\) None 0 8
3844.1.s \(\chi_{3844}(61, \cdot)\) None 0 30
3844.1.t \(\chi_{3844}(63, \cdot)\) None 0 30
3844.1.w \(\chi_{3844}(67, \cdot)\) None 0 60
3844.1.x \(\chi_{3844}(37, \cdot)\) None 0 60
3844.1.z \(\chi_{3844}(35, \cdot)\) None 0 120
3844.1.ba \(\chi_{3844}(29, \cdot)\) None 0 120
3844.1.be \(\chi_{3844}(13, \cdot)\) None 0 240
3844.1.bf \(\chi_{3844}(7, \cdot)\) None 0 240

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3844))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3844)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(961))\)\(^{\oplus 3}\)