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Properties

Label 981.1
Level 981
Weight 1
Dimension 32
Nonzero newspaces 7
Newform subspaces 8
Sturm bound 71280
Trace bound 7

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Defining parameters

Level: \( N \) = \( 981 = 3^{2} \cdot 109 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 8 \)
Sturm bound: \(71280\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(981))\).

Total New Old
Modular forms 938 514 424
Cusp forms 74 32 42
Eisenstein series 864 482 382

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 12 0

Trace form

\( 32 q + 2 q^{2} + 3 q^{3} - 3 q^{4} + 5 q^{5} - 2 q^{6} + 4 q^{7} - 3 q^{9} + O(q^{10}) \) \( 32 q + 2 q^{2} + 3 q^{3} - 3 q^{4} + 5 q^{5} - 2 q^{6} + 4 q^{7} - 3 q^{9} + 4 q^{10} + 2 q^{12} - 2 q^{13} + 4 q^{15} - 11 q^{16} - 4 q^{18} + 4 q^{19} + 3 q^{20} + 2 q^{21} + 4 q^{22} - 4 q^{25} - 8 q^{26} - 6 q^{27} - 6 q^{28} - 3 q^{29} + 2 q^{30} + 3 q^{31} + 2 q^{32} - 12 q^{34} + q^{36} + 2 q^{37} - 4 q^{39} - 2 q^{41} - q^{43} - q^{45} - 4 q^{46} - 2 q^{47} + 3 q^{48} - q^{49} - 2 q^{52} - 2 q^{54} + 6 q^{58} + 2 q^{59} + 3 q^{60} - 5 q^{61} - 4 q^{62} + 4 q^{63} + 6 q^{64} + 2 q^{65} - 2 q^{75} - 4 q^{76} - 4 q^{78} - 4 q^{80} - 3 q^{81} + 12 q^{82} + 3 q^{83} - 2 q^{84} - 2 q^{86} - 3 q^{87} + 4 q^{89} - 2 q^{90} - 18 q^{91} - 2 q^{93} - 4 q^{94} + 4 q^{96} - 3 q^{97} + 4 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(981))\)

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
981.1.b \(\chi_{981}(764, \cdot)\) None 0 1
981.1.d \(\chi_{981}(980, \cdot)\) 981.1.d.a 2 1
981.1.d.b 2
981.1.j \(\chi_{981}(469, \cdot)\) 981.1.j.a 2 2
981.1.l \(\chi_{981}(917, \cdot)\) 981.1.l.a 4 2
981.1.m \(\chi_{981}(173, \cdot)\) None 0 2
981.1.n \(\chi_{981}(326, \cdot)\) 981.1.n.a 2 2
981.1.o \(\chi_{981}(155, \cdot)\) None 0 2
981.1.p \(\chi_{981}(263, \cdot)\) None 0 2
981.1.s \(\chi_{981}(110, \cdot)\) None 0 2
981.1.t \(\chi_{981}(281, \cdot)\) None 0 2
981.1.v \(\chi_{981}(809, \cdot)\) None 0 2
981.1.z \(\chi_{981}(226, \cdot)\) 981.1.z.a 4 4
981.1.bc \(\chi_{981}(76, \cdot)\) 981.1.bc.a 4 4
981.1.bd \(\chi_{981}(646, \cdot)\) None 0 4
981.1.bg \(\chi_{981}(259, \cdot)\) None 0 4
981.1.bh \(\chi_{981}(245, \cdot)\) None 0 6
981.1.bj \(\chi_{981}(71, \cdot)\) None 0 6
981.1.bk \(\chi_{981}(311, \cdot)\) None 0 6
981.1.bl \(\chi_{981}(125, \cdot)\) None 0 6
981.1.bm \(\chi_{981}(38, \cdot)\) None 0 6
981.1.bp \(\chi_{981}(113, \cdot)\) None 0 6
981.1.bt \(\chi_{981}(382, \cdot)\) None 0 12
981.1.bw \(\chi_{981}(220, \cdot)\) None 0 12
981.1.bx \(\chi_{981}(19, \cdot)\) 981.1.bx.a 12 12
981.1.bz \(\chi_{981}(170, \cdot)\) None 0 18
981.1.ca \(\chi_{981}(74, \cdot)\) None 0 18
981.1.cb \(\chi_{981}(20, \cdot)\) None 0 18
981.1.cc \(\chi_{981}(131, \cdot)\) None 0 18
981.1.cf \(\chi_{981}(5, \cdot)\) None 0 18
981.1.ch \(\chi_{981}(26, \cdot)\) None 0 18
981.1.cj \(\chi_{981}(52, \cdot)\) None 0 36
981.1.ck \(\chi_{981}(13, \cdot)\) None 0 36
981.1.cn \(\chi_{981}(10, \cdot)\) None 0 36

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(981))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(981)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(327))\)\(^{\oplus 2}\)