Properties

Label 2015.1.h
Level 2015
Weight 1
Character orbit h
Rep. character \(\chi_{2015}(2014,\cdot)\)
Character field \(\Q\)
Dimension 28
Newform subspaces 5
Sturm bound 224
Trace bound 3

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2015.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2015 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(224\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2015, [\chi])\).

Total New Old
Modular forms 32 32 0
Cusp forms 28 28 0
Eisenstein series 4 4 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 28 0 0 0

Trace form

\( 28q + 16q^{4} + 24q^{9} + O(q^{10}) \) \( 28q + 16q^{4} + 24q^{9} - 4q^{10} - 8q^{14} + 20q^{16} + 20q^{25} - 4q^{35} + 4q^{36} - 8q^{40} + 16q^{49} - 16q^{56} + 8q^{64} - 16q^{66} - 16q^{69} + 12q^{81} - 12q^{90} - 8q^{94} - 8q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2015, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2015.1.h.a \(4\) \(1.006\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-155}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+q^{9}+\cdots\)
2015.1.h.b \(6\) \(1.006\) \(\Q(\zeta_{26})^+\) \(D_{13}\) \(\Q(\sqrt{-2015}) \) None \(-1\) \(-1\) \(6\) \(-1\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
2015.1.h.c \(6\) \(1.006\) \(\Q(\zeta_{26})^+\) \(D_{13}\) \(\Q(\sqrt{-2015}) \) None \(-1\) \(1\) \(6\) \(-1\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
2015.1.h.d \(6\) \(1.006\) \(\Q(\zeta_{26})^+\) \(D_{13}\) \(\Q(\sqrt{-2015}) \) None \(1\) \(-1\) \(-6\) \(1\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
2015.1.h.e \(6\) \(1.006\) \(\Q(\zeta_{26})^+\) \(D_{13}\) \(\Q(\sqrt{-2015}) \) None \(1\) \(1\) \(-6\) \(1\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + T^{2} )^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))
$3$ (\( ( 1 + T^{4} )^{2} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))
$5$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{6} \))
$7$ (\( ( 1 + T^{2} )^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))
$11$ (\( ( 1 + T^{2} )^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))
$13$ (\( 1 + T^{4} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{6} \))
$17$ (\( ( 1 + T^{4} )^{2} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))
$19$ (\( ( 1 + T^{2} )^{4} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))
$23$ (\( ( 1 + T^{4} )^{2} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))
$29$ (\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))
$31$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))
$37$ (\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))
$41$ (\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))
$43$ (\( ( 1 + T^{4} )^{2} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))
$47$ (\( ( 1 + T^{2} )^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))
$53$ (\( ( 1 + T^{4} )^{2} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))
$59$ (\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))
$61$ (\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))
$67$ (\( ( 1 + T^{2} )^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))
$71$ (\( ( 1 + T^{2} )^{4} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))
$73$ (\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))
$79$ (\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))
$83$ (\( ( 1 + T^{4} )^{2} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))
$89$ (\( ( 1 + T^{2} )^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))
$97$ (\( ( 1 + T^{2} )^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} + T^{7} + T^{8} + T^{9} + T^{10} + T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))(\( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} - T^{7} + T^{8} - T^{9} + T^{10} - T^{11} + T^{12} \))
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