Properties

Label 176.2.a
Level $176$
Weight $2$
Character orbit 176.a
Rep. character $\chi_{176}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 176 = 2^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 176.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(176))\).

Total New Old
Modular forms 30 5 25
Cusp forms 19 5 14
Eisenstein series 11 0 11

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

\(2\)\(11\)FrickeDim.
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(4\)

Trace form

\( 5 q + 2 q^{3} - 2 q^{5} + 4 q^{7} + 5 q^{9} + O(q^{10}) \) \( 5 q + 2 q^{3} - 2 q^{5} + 4 q^{7} + 5 q^{9} + 3 q^{11} - 2 q^{13} + 2 q^{15} + 2 q^{17} - 4 q^{19} - 8 q^{21} - 6 q^{23} + 7 q^{25} + 2 q^{27} - 10 q^{29} + 2 q^{31} - 12 q^{35} - 10 q^{37} - 8 q^{39} + 2 q^{41} + 16 q^{43} - 18 q^{45} - 16 q^{47} + 13 q^{49} - 28 q^{51} - 2 q^{53} - 4 q^{55} - 8 q^{57} - 2 q^{59} + 6 q^{61} + 32 q^{63} - 4 q^{65} - 2 q^{67} + 8 q^{69} - 10 q^{71} + 18 q^{73} + 28 q^{75} + 20 q^{79} - 3 q^{81} - 8 q^{83} + 4 q^{85} - 40 q^{87} + 14 q^{89} + 48 q^{91} + 24 q^{93} + 48 q^{95} + 6 q^{97} + 9 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(176))\) 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 11
176.2.a.a 176.a 1.a $1$ $1.405$ \(\Q\) None \(0\) \(-1\) \(-3\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-2q^{7}-2q^{9}+q^{11}+\cdots\)
176.2.a.b 176.a 1.a $1$ $1.405$ \(\Q\) None \(0\) \(1\) \(1\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots\)
176.2.a.c 176.a 1.a $1$ $1.405$ \(\Q\) None \(0\) \(3\) \(-3\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-3q^{5}+2q^{7}+6q^{9}+q^{11}+\cdots\)
176.2.a.d 176.a 1.a $2$ $1.405$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(3\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(2-\beta )q^{5}+2\beta q^{7}+(1+\beta )q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(176))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(176)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)