Properties

Label 179.2.a
Level $179$
Weight $2$
Character orbit 179.a
Rep. character $\chi_{179}(1,\cdot)$
Character field $\Q$
Dimension $15$
Newform subspaces $3$
Sturm bound $30$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 179 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 179.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(30\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(179))\).

Total New Old
Modular forms 16 16 0
Cusp forms 15 15 0
Eisenstein series 1 1 0

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

\(179\)Dim
\(+\)\(3\)
\(-\)\(12\)

Trace form

\( 15 q - 2 q^{2} - 2 q^{3} + 16 q^{4} + 2 q^{5} - 4 q^{6} - 6 q^{8} + 11 q^{9} + O(q^{10}) \) \( 15 q - 2 q^{2} - 2 q^{3} + 16 q^{4} + 2 q^{5} - 4 q^{6} - 6 q^{8} + 11 q^{9} + 6 q^{10} - 8 q^{11} - 4 q^{12} + 12 q^{13} + 4 q^{14} - 2 q^{15} + 14 q^{16} + 10 q^{17} - 8 q^{18} + 8 q^{19} - 12 q^{20} + 16 q^{21} - 10 q^{22} + 6 q^{23} + 2 q^{24} + 9 q^{25} - 8 q^{26} - 14 q^{27} - 10 q^{28} + 8 q^{29} - 24 q^{30} + 4 q^{31} - 34 q^{32} - 12 q^{33} - 12 q^{34} - 14 q^{35} - 14 q^{36} - 20 q^{38} - 14 q^{39} + 2 q^{40} - 4 q^{41} - 62 q^{42} + 14 q^{43} - 38 q^{44} + q^{45} - 12 q^{46} + 15 q^{47} - 32 q^{48} + 23 q^{49} + 2 q^{50} - q^{51} + 36 q^{52} - 20 q^{53} + 4 q^{54} + 4 q^{55} - 6 q^{56} - 5 q^{57} - 2 q^{58} - 16 q^{59} + 16 q^{60} + 46 q^{61} - 12 q^{62} - 4 q^{63} + 44 q^{64} + 27 q^{65} + 18 q^{66} + 18 q^{67} + 26 q^{68} + 16 q^{69} - 4 q^{70} - 26 q^{71} - 24 q^{72} - 6 q^{73} + 18 q^{74} - 29 q^{75} + 72 q^{76} + 16 q^{77} + 6 q^{78} - 14 q^{79} - 18 q^{80} + 31 q^{81} - 2 q^{82} + 8 q^{83} + 50 q^{84} - 2 q^{85} - 20 q^{86} - 25 q^{87} - 30 q^{88} + 6 q^{89} + 56 q^{90} + 10 q^{91} + 42 q^{92} + 20 q^{93} + 32 q^{94} - 10 q^{95} + 72 q^{96} - 2 q^{97} - 64 q^{98} - 18 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(179))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 179
179.2.a.a 179.a 1.a $1$ $1.429$ \(\Q\) None \(2\) \(0\) \(3\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+3q^{5}-4q^{7}-3q^{9}+\cdots\)
179.2.a.b 179.a 1.a $3$ $1.429$ \(\Q(\zeta_{14})^+\) None \(-1\) \(-2\) \(-4\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots\)
179.2.a.c 179.a 1.a $11$ $1.429$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-3\) \(0\) \(3\) \(8\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)