Properties

Label 152.2.a
Level $152$
Weight $2$
Character orbit 152.a
Rep. character $\chi_{152}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $3$
Sturm bound $40$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 152.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(152))\).

Total New Old
Modular forms 24 5 19
Cusp forms 17 5 12
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(1\)
Minus space\(-\)\(4\)

Trace form

\( 5 q + 4 q^{7} + 11 q^{9} + O(q^{10}) \) \( 5 q + 4 q^{7} + 11 q^{9} - 6 q^{11} + 2 q^{13} - 8 q^{15} + 2 q^{17} - 3 q^{19} - 6 q^{23} - 3 q^{25} - 10 q^{29} + 12 q^{31} - 4 q^{33} - 6 q^{35} - 14 q^{37} - 10 q^{39} + 6 q^{41} + 2 q^{43} - 28 q^{45} - 18 q^{47} + 9 q^{49} - 4 q^{51} + 2 q^{53} + 22 q^{55} + 2 q^{57} - 8 q^{59} + 12 q^{61} + 38 q^{63} + 16 q^{65} + 28 q^{67} - 44 q^{69} - 8 q^{71} - 2 q^{73} + 36 q^{75} - 2 q^{77} + 12 q^{79} + 37 q^{81} + 8 q^{83} + 6 q^{85} - 10 q^{87} + 6 q^{89} + 32 q^{91} - 12 q^{93} + 22 q^{97} - 58 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(152))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 19
152.2.a.a 152.a 1.a $1$ $1.214$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
152.2.a.b 152.a 1.a $1$ $1.214$ \(\Q\) None \(0\) \(1\) \(0\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}-2q^{9}+2q^{11}+q^{13}+\cdots\)
152.2.a.c 152.a 1.a $3$ $1.214$ 3.3.961.1 None \(0\) \(1\) \(1\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(152))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(152)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 2}\)