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Properties

Label 2301.1
Level 2301
Weight 1
Dimension 112
Nonzero newspaces 1
Newform subspaces 3
Sturm bound 389760
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2301 = 3 \cdot 13 \cdot 59 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 3 \)
Sturm bound: \(389760\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2301))\).

Total New Old
Modular forms 2922 1368 1554
Cusp forms 138 112 26
Eisenstein series 2784 1256 1528

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 112 0 0 0

Trace form

\( 112 q - 4 q^{4} - 4 q^{9} - 8 q^{10} - 8 q^{12} - 12 q^{16} - 8 q^{22} - 4 q^{25} - 8 q^{30} - 4 q^{36} - 4 q^{39} - 16 q^{40} - 8 q^{43} - 8 q^{48} - 4 q^{49} - 8 q^{52} - 8 q^{55} - 12 q^{64} - 8 q^{66}+ \cdots - 8 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2301))\)

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
2301.1.c \(\chi_{2301}(1535, \cdot)\) None 0 1
2301.1.e \(\chi_{2301}(235, \cdot)\) None 0 1
2301.1.f \(\chi_{2301}(766, \cdot)\) None 0 1
2301.1.h \(\chi_{2301}(2066, \cdot)\) None 0 1
2301.1.k \(\chi_{2301}(1240, \cdot)\) None 0 2
2301.1.m \(\chi_{2301}(707, \cdot)\) None 0 2
2301.1.o \(\chi_{2301}(589, \cdot)\) None 0 2
2301.1.p \(\chi_{2301}(296, \cdot)\) None 0 2
2301.1.q \(\chi_{2301}(1004, \cdot)\) None 0 2
2301.1.s \(\chi_{2301}(412, \cdot)\) None 0 2
2301.1.v \(\chi_{2301}(176, \cdot)\) None 0 4
2301.1.x \(\chi_{2301}(709, \cdot)\) None 0 4
2301.1.z \(\chi_{2301}(116, \cdot)\) 2301.1.z.a 28 28
2301.1.z.b 28
2301.1.z.c 56
2301.1.bb \(\chi_{2301}(103, \cdot)\) None 0 28
2301.1.bc \(\chi_{2301}(40, \cdot)\) None 0 28
2301.1.be \(\chi_{2301}(53, \cdot)\) None 0 28
2301.1.bh \(\chi_{2301}(8, \cdot)\) None 0 56
2301.1.bj \(\chi_{2301}(112, \cdot)\) None 0 56
2301.1.bm \(\chi_{2301}(55, \cdot)\) None 0 56
2301.1.bo \(\chi_{2301}(29, \cdot)\) None 0 56
2301.1.bp \(\chi_{2301}(17, \cdot)\) None 0 56
2301.1.bq \(\chi_{2301}(10, \cdot)\) None 0 56
2301.1.bs \(\chi_{2301}(7, \cdot)\) None 0 112
2301.1.bu \(\chi_{2301}(2, \cdot)\) None 0 112

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2301))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2301)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(767))\)\(^{\oplus 2}\)