Properties

Label 1225.1.g
Level 1225
Weight 1
Character orbit g
Rep. character \(\chi_{1225}(393,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 6
Newform subspaces 2
Sturm bound 140
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1225.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(140\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1225, [\chi])\).

Total New Old
Modular forms 54 16 38
Cusp forms 6 6 0
Eisenstein series 48 10 38

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6q + O(q^{10}) \) \( 6q - 6q^{16} - 6q^{36} + 12q^{46} - 6q^{81} + 12q^{86} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1225, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1225.1.g.a \(2\) \(0.611\) \(\Q(\sqrt{-1}) \) \(D_{2}\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{4}+iq^{9}+q^{11}-q^{16}-iq^{29}+\cdots\)
1225.1.g.b \(4\) \(0.611\) \(\Q(i, \sqrt{6})\) \(D_{6}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+2\beta _{2}q^{4}-\beta _{3}q^{8}+\beta _{2}q^{9}+\cdots\)

Hecke characteristic polynomials

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