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Properties

Label 495.1
Level 495
Weight 1
Dimension 17
Nonzero newspaces 3
Newform subspaces 7
Sturm bound 17280
Trace bound 1

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Defining parameters

Level: \( N \) = \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 7 \)
Sturm bound: \(17280\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(495))\).

Total New Old
Modular forms 672 259 413
Cusp forms 32 17 15
Eisenstein series 640 242 398

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 17 0 0 0

Trace form

\( 17 q + 2 q^{3} + 5 q^{4} - 2 q^{9} + O(q^{10}) \) \( 17 q + 2 q^{3} + 5 q^{4} - 2 q^{9} + 3 q^{11} - 2 q^{12} - q^{15} - q^{16} - 6 q^{20} + 4 q^{25} - 4 q^{27} - 4 q^{31} + 4 q^{33} - 8 q^{34} - 4 q^{36} - 4 q^{37} + 3 q^{44} + 2 q^{45} - 6 q^{47} + 4 q^{48} + 5 q^{49} - 9 q^{55} - 2 q^{60} - 9 q^{64} - 2 q^{67} - 8 q^{70} - 6 q^{71} - 2 q^{75} + 3 q^{80} - 6 q^{81} - 6 q^{89} - 8 q^{91} - 6 q^{93} - 2 q^{97} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(495))\)

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
495.1.b \(\chi_{495}(406, \cdot)\) None 0 1
495.1.e \(\chi_{495}(386, \cdot)\) None 0 1
495.1.g \(\chi_{495}(89, \cdot)\) None 0 1
495.1.h \(\chi_{495}(109, \cdot)\) 495.1.h.a 1 1
495.1.h.b 2
495.1.h.c 2
495.1.j \(\chi_{495}(298, \cdot)\) None 0 2
495.1.m \(\chi_{495}(98, \cdot)\) None 0 2
495.1.o \(\chi_{495}(274, \cdot)\) 495.1.o.a 2 2
495.1.o.b 2
495.1.q \(\chi_{495}(254, \cdot)\) None 0 2
495.1.s \(\chi_{495}(56, \cdot)\) None 0 2
495.1.t \(\chi_{495}(76, \cdot)\) None 0 2
495.1.v \(\chi_{495}(19, \cdot)\) None 0 4
495.1.w \(\chi_{495}(179, \cdot)\) None 0 4
495.1.y \(\chi_{495}(26, \cdot)\) None 0 4
495.1.bb \(\chi_{495}(46, \cdot)\) None 0 4
495.1.bd \(\chi_{495}(32, \cdot)\) 495.1.bd.a 4 4
495.1.bd.b 4
495.1.be \(\chi_{495}(67, \cdot)\) None 0 4
495.1.bh \(\chi_{495}(8, \cdot)\) None 0 8
495.1.bk \(\chi_{495}(37, \cdot)\) None 0 8
495.1.bm \(\chi_{495}(61, \cdot)\) None 0 8
495.1.bn \(\chi_{495}(86, \cdot)\) None 0 8
495.1.bp \(\chi_{495}(14, \cdot)\) None 0 8
495.1.br \(\chi_{495}(79, \cdot)\) None 0 8
495.1.bt \(\chi_{495}(58, \cdot)\) None 0 16
495.1.bu \(\chi_{495}(2, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(495))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(495)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)