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Properties

Label 1359.1
Level 1359
Weight 1
Dimension 34
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 136800
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1359 = 3^{2} \cdot 151 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(136800\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1359))\).

Total New Old
Modular forms 1299 705 594
Cusp forms 99 34 65
Eisenstein series 1200 671 529

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 34 0 0 0

Trace form

\( 34 q + q^{2} + 10 q^{4} + q^{5} + 2 q^{8} + O(q^{10}) \) \( 34 q + q^{2} + 10 q^{4} + q^{5} + 2 q^{8} - 2 q^{10} + q^{11} + 7 q^{16} + q^{17} - 3 q^{19} + 3 q^{20} - 2 q^{22} + 10 q^{25} + q^{29} - 3 q^{31} + 3 q^{32} - 2 q^{34} - 3 q^{37} - 5 q^{38} - 11 q^{40} + q^{43} - 4 q^{44} + q^{47} + 9 q^{49} - 4 q^{50} - 2 q^{55} - 9 q^{58} + q^{59} + 2 q^{62} + 8 q^{64} - 4 q^{68} + 2 q^{74} - q^{76} - 2 q^{80} - 2 q^{85} + 2 q^{86} - 4 q^{88} - 9 q^{94} + 2 q^{95} - 3 q^{97} + q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1359))\)

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
1359.1.c \(\chi_{1359}(152, \cdot)\) None 0 1
1359.1.d \(\chi_{1359}(1207, \cdot)\) 1359.1.d.a 1 1
1359.1.d.b 3
1359.1.d.c 6
1359.1.k \(\chi_{1359}(938, \cdot)\) None 0 2
1359.1.l \(\chi_{1359}(874, \cdot)\) None 0 2
1359.1.m \(\chi_{1359}(301, \cdot)\) None 0 2
1359.1.n \(\chi_{1359}(637, \cdot)\) None 0 2
1359.1.o \(\chi_{1359}(32, \cdot)\) None 0 2
1359.1.q \(\chi_{1359}(269, \cdot)\) None 0 2
1359.1.r \(\chi_{1359}(605, \cdot)\) None 0 2
1359.1.u \(\chi_{1359}(184, \cdot)\) None 0 2
1359.1.v \(\chi_{1359}(8, \cdot)\) None 0 4
1359.1.x \(\chi_{1359}(847, \cdot)\) 1359.1.x.a 4 4
1359.1.bd \(\chi_{1359}(155, \cdot)\) None 0 8
1359.1.bf \(\chi_{1359}(286, \cdot)\) None 0 8
1359.1.bg \(\chi_{1359}(238, \cdot)\) None 0 8
1359.1.bh \(\chi_{1359}(46, \cdot)\) None 0 8
1359.1.bk \(\chi_{1359}(59, \cdot)\) None 0 8
1359.1.bl \(\chi_{1359}(620, \cdot)\) None 0 8
1359.1.bn \(\chi_{1359}(2, \cdot)\) None 0 8
1359.1.bo \(\chi_{1359}(778, \cdot)\) None 0 8
1359.1.bp \(\chi_{1359}(28, \cdot)\) 1359.1.bp.a 20 20
1359.1.br \(\chi_{1359}(44, \cdot)\) None 0 20
1359.1.bw \(\chi_{1359}(61, \cdot)\) None 0 40
1359.1.by \(\chi_{1359}(20, \cdot)\) None 0 40
1359.1.bz \(\chi_{1359}(17, \cdot)\) None 0 40
1359.1.cc \(\chi_{1359}(11, \cdot)\) None 0 40
1359.1.cd \(\chi_{1359}(82, \cdot)\) None 0 40
1359.1.ce \(\chi_{1359}(67, \cdot)\) None 0 40
1359.1.cf \(\chi_{1359}(7, \cdot)\) None 0 40
1359.1.cg \(\chi_{1359}(5, \cdot)\) None 0 40

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1359))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1359)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(453))\)\(^{\oplus 2}\)