Properties

Label 1225.1
Level 1225
Weight 1
Dimension 26
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 117600
Trace bound 9

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Defining parameters

Level: \( N \) = \( 1225\( 1225 = 5^{2} \cdot 7^{2} \) \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(117600\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1225))\).

Total New Old
Modular forms 1714 1020 694
Cusp forms 34 26 8
Eisenstein series 1680 994 686

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 26 0 0 0

Trace form

\( 26q + O(q^{10}) \) \( 26q + 4q^{11} + 4q^{16} - 18q^{36} - 4q^{46} - 8q^{71} - 4q^{81} - 4q^{86} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1225))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1225.1.c \(\chi_{1225}(1224, \cdot)\) None 0 1
1225.1.d \(\chi_{1225}(1126, \cdot)\) None 0 1
1225.1.g \(\chi_{1225}(393, \cdot)\) 1225.1.g.a 2 2
1225.1.g.b 4
1225.1.i \(\chi_{1225}(276, \cdot)\) 1225.1.i.a 2 2
1225.1.i.b 2
1225.1.j \(\chi_{1225}(374, \cdot)\) 1225.1.j.a 4 2
1225.1.m \(\chi_{1225}(146, \cdot)\) None 0 4
1225.1.n \(\chi_{1225}(244, \cdot)\) None 0 4
1225.1.q \(\chi_{1225}(18, \cdot)\) 1225.1.q.a 4 4
1225.1.q.b 8
1225.1.r \(\chi_{1225}(76, \cdot)\) None 0 6
1225.1.s \(\chi_{1225}(174, \cdot)\) None 0 6
1225.1.v \(\chi_{1225}(148, \cdot)\) None 0 8
1225.1.y \(\chi_{1225}(43, \cdot)\) None 0 12
1225.1.bb \(\chi_{1225}(19, \cdot)\) None 0 8
1225.1.bc \(\chi_{1225}(31, \cdot)\) None 0 8
1225.1.bf \(\chi_{1225}(24, \cdot)\) None 0 12
1225.1.bg \(\chi_{1225}(26, \cdot)\) None 0 12
1225.1.bh \(\chi_{1225}(67, \cdot)\) None 0 16
1225.1.bk \(\chi_{1225}(34, \cdot)\) None 0 24
1225.1.bl \(\chi_{1225}(6, \cdot)\) None 0 24
1225.1.bm \(\chi_{1225}(32, \cdot)\) None 0 24
1225.1.bq \(\chi_{1225}(8, \cdot)\) None 0 48
1225.1.br \(\chi_{1225}(61, \cdot)\) None 0 48
1225.1.bs \(\chi_{1225}(54, \cdot)\) None 0 48
1225.1.bv \(\chi_{1225}(2, \cdot)\) None 0 96

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1225))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1225)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T^{4} \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 + T )^{2}( 1 - T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \))
$3$ (\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 - T^{4} + T^{8} )^{2} \))
$5$ 1
$7$ 1
$11$ (\( ( 1 - T )^{4} \))(\( ( 1 + T + T^{2} )^{4} \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{4}( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{4} \))(\( ( 1 - T )^{8}( 1 + T + T^{2} )^{4} \))
$13$ (\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{4} \))
$17$ (\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 - T^{4} + T^{8} )^{2} \))
$19$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{4}( 1 + T + T^{2} )^{4} \))
$23$ (\( 1 + T^{4} \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 + T )^{2}( 1 - T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \))
$29$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 - T^{2} + T^{4} )^{4} \))
$31$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{4} \))
$37$ (\( 1 + T^{4} \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 + T )^{2}( 1 - T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \))
$41$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{8} \))
$43$ (\( 1 + T^{4} \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T^{4} + T^{8} )^{2} \))
$47$ (\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 - T^{4} + T^{8} )^{2} \))
$53$ (\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 - T^{4} + T^{8} )^{2} \))
$59$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{4}( 1 + T + T^{2} )^{4} \))
$61$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{4} \))
$67$ (\( 1 + T^{4} \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 + T )^{2}( 1 - T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} ) \))
$71$ (\( ( 1 + T )^{4} \))(\( ( 1 - T + T^{2} )^{4} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{4} \))(\( ( 1 + T )^{8} \))(\( ( 1 - T + T^{2} )^{8} \))
$73$ (\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( 1 - T^{4} + T^{8} \))(\( ( 1 - T^{4} + T^{8} )^{2} \))
$79$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T + T^{2} ) \))(\( ( 1 + T )^{4}( 1 - T + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2} \))
$83$ (\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{4} \))
$89$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{4}( 1 + T + T^{2} )^{4} \))
$97$ (\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{4} \))
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