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Properties

Label 451.1
Level 451
Weight 1
Dimension 6
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 16800
Trace bound 1

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Defining parameters

Level: \( N \) = \( 451 = 11 \cdot 41 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(16800\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(451))\).

Total New Old
Modular forms 406 356 50
Cusp forms 6 6 0
Eisenstein series 400 350 50

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 4 0

Trace form

\( 6 q + 6 q^{4} - 2 q^{5} + 2 q^{9} + O(q^{10}) \) \( 6 q + 6 q^{4} - 2 q^{5} + 2 q^{9} - 4 q^{14} - 2 q^{16} - 2 q^{20} + 4 q^{22} + 2 q^{23} - 6 q^{31} - 4 q^{34} + 2 q^{36} + 2 q^{37} - 4 q^{38} + 2 q^{45} - 4 q^{47} + 4 q^{53} - 4 q^{58} - 6 q^{59} - 2 q^{64} - 4 q^{70} - 4 q^{71} - 2 q^{77} - 2 q^{80} - 2 q^{81} + 4 q^{82} - 4 q^{89} - 4 q^{91} + 2 q^{92} + 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(451))\)

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
451.1.b \(\chi_{451}(450, \cdot)\) 451.1.b.a 1 1
451.1.b.b 1
451.1.c \(\chi_{451}(329, \cdot)\) None 0 1
451.1.f \(\chi_{451}(32, \cdot)\) 451.1.f.a 4 2
451.1.n \(\chi_{451}(232, \cdot)\) None 0 4
451.1.o \(\chi_{451}(303, \cdot)\) None 0 4
451.1.p \(\chi_{451}(195, \cdot)\) None 0 4
451.1.v \(\chi_{451}(230, \cdot)\) None 0 4
451.1.w \(\chi_{451}(51, \cdot)\) None 0 4
451.1.x \(\chi_{451}(18, \cdot)\) None 0 4
451.1.y \(\chi_{451}(83, \cdot)\) None 0 4
451.1.z \(\chi_{451}(139, \cdot)\) None 0 4
451.1.ba \(\chi_{451}(40, \cdot)\) None 0 4
451.1.bb \(\chi_{451}(107, \cdot)\) None 0 4
451.1.bc \(\chi_{451}(105, \cdot)\) None 0 4
451.1.bd \(\chi_{451}(72, \cdot)\) None 0 4
451.1.be \(\chi_{451}(10, \cdot)\) None 0 4
451.1.bh \(\chi_{451}(46, \cdot)\) None 0 8
451.1.bi \(\chi_{451}(21, \cdot)\) None 0 8
451.1.bj \(\chi_{451}(50, \cdot)\) None 0 8
451.1.bk \(\chi_{451}(39, \cdot)\) None 0 8
451.1.bl \(\chi_{451}(84, \cdot)\) None 0 8
451.1.br \(\chi_{451}(2, \cdot)\) None 0 8
451.1.bs \(\chi_{451}(15, \cdot)\) None 0 16
451.1.bv \(\chi_{451}(12, \cdot)\) None 0 16
451.1.bw \(\chi_{451}(136, \cdot)\) None 0 16
451.1.bx \(\chi_{451}(75, \cdot)\) None 0 16
451.1.by \(\chi_{451}(47, \cdot)\) None 0 16
451.1.cd \(\chi_{451}(3, \cdot)\) None 0 16