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Properties

Label 964.1
Level 964
Weight 1
Dimension 63
Nonzero newspaces 11
Newform subspaces 14
Sturm bound 58080
Trace bound 2

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Defining parameters

Level: \( N \) = \( 964 = 2^{2} \cdot 241 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 11 \)
Newform subspaces: \( 14 \)
Sturm bound: \(58080\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(964))\).

Total New Old
Modular forms 663 301 362
Cusp forms 63 63 0
Eisenstein series 600 238 362

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 63 0 0 0

Trace form

\( 63 q - q^{2} + 3 q^{4} - 2 q^{5} - q^{8} + 3 q^{9} + O(q^{10}) \) \( 63 q - q^{2} + 3 q^{4} - 2 q^{5} - q^{8} + 3 q^{9} - 6 q^{10} - 2 q^{13} + 3 q^{16} - 2 q^{17} - q^{18} - 2 q^{20} - 3 q^{25} - 2 q^{26} - 6 q^{29} - q^{32} - 2 q^{34} + 3 q^{36} - 2 q^{37} - 6 q^{40} - 6 q^{41} - 2 q^{45} + 3 q^{49} - 3 q^{50} - 2 q^{52} - 6 q^{53} - 2 q^{58} - 2 q^{61} + 3 q^{64} - 4 q^{65} - 2 q^{68} - q^{72} - 2 q^{73} - 2 q^{74} - 4 q^{77} - 2 q^{80} + 3 q^{81} - 2 q^{82} - 4 q^{85} - 2 q^{89} - 6 q^{90} - 6 q^{97} - 5 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(964))\)

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
964.1.b \(\chi_{964}(483, \cdot)\) None 0 1
964.1.c \(\chi_{964}(963, \cdot)\) 964.1.c.a 1 1
964.1.c.b 1
964.1.c.c 1
964.1.c.d 2
964.1.g \(\chi_{964}(659, \cdot)\) 964.1.g.a 2 2
964.1.j \(\chi_{964}(467, \cdot)\) 964.1.j.a 2 2
964.1.k \(\chi_{964}(15, \cdot)\) 964.1.k.a 2 2
964.1.l \(\chi_{964}(211, \cdot)\) None 0 4
964.1.o \(\chi_{964}(143, \cdot)\) 964.1.o.a 4 4
964.1.p \(\chi_{964}(87, \cdot)\) 964.1.p.a 4 4
964.1.q \(\chi_{964}(663, \cdot)\) 964.1.q.a 4 4
964.1.u \(\chi_{964}(165, \cdot)\) None 0 8
964.1.v \(\chi_{964}(135, \cdot)\) 964.1.v.a 8 8
964.1.y \(\chi_{964}(239, \cdot)\) None 0 8
964.1.z \(\chi_{964}(119, \cdot)\) 964.1.z.a 8 8
964.1.ba \(\chi_{964}(147, \cdot)\) 964.1.ba.a 8 8
964.1.bc \(\chi_{964}(27, \cdot)\) None 0 16
964.1.be \(\chi_{964}(65, \cdot)\) None 0 16
964.1.bh \(\chi_{964}(83, \cdot)\) 964.1.bh.a 16 16
964.1.bj \(\chi_{964}(17, \cdot)\) None 0 32
964.1.bl \(\chi_{964}(3, \cdot)\) None 0 32
964.1.bm \(\chi_{964}(13, \cdot)\) None 0 64