Properties

Label 152.1
Level 152
Weight 1
Dimension 10
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 1440
Trace bound 2

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(1440\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(152))\).

Total New Old
Modular forms 120 44 76
Cusp forms 12 10 2
Eisenstein series 108 34 74

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

\( 10q - q^{2} - 2q^{3} + q^{4} - 4q^{6} - 2q^{7} - q^{8} - 3q^{9} + O(q^{10}) \) \( 10q - q^{2} - 2q^{3} + q^{4} - 4q^{6} - 2q^{7} - q^{8} - 3q^{9} - 2q^{11} - 2q^{12} + q^{16} - 4q^{17} + 6q^{18} - q^{19} + 7q^{22} - 2q^{23} - 4q^{24} + q^{25} - 2q^{26} + 5q^{27} - 2q^{28} - q^{32} - 4q^{33} - 2q^{34} - 3q^{36} + q^{38} + 2q^{39} - 2q^{41} + 2q^{42} - 2q^{43} + 7q^{44} + 4q^{47} + 7q^{48} - q^{49} - q^{50} + 5q^{51} - 2q^{54} - 4q^{57} - 2q^{58} - 2q^{59} + q^{64} - 4q^{66} - 2q^{67} + 5q^{68} + 6q^{72} + 5q^{73} + 4q^{74} - 2q^{75} - q^{76} + 2q^{81} - 2q^{82} - 2q^{83} - 2q^{86} + 2q^{87} - 2q^{88} - 2q^{89} - 2q^{92} - 4q^{96} - 2q^{97} - q^{98} + 3q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(152))\)

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
152.1.d \(\chi_{152}(39, \cdot)\) None 0 1
152.1.e \(\chi_{152}(113, \cdot)\) None 0 1
152.1.f \(\chi_{152}(115, \cdot)\) None 0 1
152.1.g \(\chi_{152}(37, \cdot)\) 152.1.g.a 1 1
152.1.g.b 1
152.1.k \(\chi_{152}(11, \cdot)\) 152.1.k.a 2 2
152.1.l \(\chi_{152}(69, \cdot)\) None 0 2
152.1.m \(\chi_{152}(7, \cdot)\) None 0 2
152.1.n \(\chi_{152}(65, \cdot)\) None 0 2
152.1.r \(\chi_{152}(33, \cdot)\) None 0 6
152.1.s \(\chi_{152}(13, \cdot)\) None 0 6
152.1.u \(\chi_{152}(35, \cdot)\) 152.1.u.a 6 6
152.1.x \(\chi_{152}(23, \cdot)\) None 0 6

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(152))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(152)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

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