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Properties

Label 161.4.a
Level $161$
Weight $4$
Character orbit 161.a
Rep. character $\chi_{161}(1,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $4$
Sturm bound $64$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 161 = 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 161.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(161))\).

Total New Old
Modular forms 50 34 16
Cusp forms 46 34 12
Eisenstein series 4 0 4

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

\(7\)\(23\)FrickeDim
\(+\)\(+\)$+$\(9\)
\(+\)\(-\)$-$\(8\)
\(-\)\(+\)$-$\(5\)
\(-\)\(-\)$+$\(12\)
Plus space\(+\)\(21\)
Minus space\(-\)\(13\)

Trace form

\( 34 q - 4 q^{3} + 144 q^{4} - 16 q^{5} - 10 q^{6} - 6 q^{8} + 434 q^{9} + O(q^{10}) \) \( 34 q - 4 q^{3} + 144 q^{4} - 16 q^{5} - 10 q^{6} - 6 q^{8} + 434 q^{9} + 152 q^{10} - 92 q^{11} - 78 q^{12} - 168 q^{13} - 40 q^{15} + 496 q^{16} - 140 q^{17} + 34 q^{18} + 180 q^{19} + 100 q^{20} - 112 q^{21} - 360 q^{22} + 138 q^{23} + 468 q^{24} + 406 q^{25} + 286 q^{26} - 268 q^{27} - 156 q^{29} + 16 q^{30} + 240 q^{31} + 1032 q^{32} + 608 q^{33} - 540 q^{34} + 280 q^{35} + 2094 q^{36} + 872 q^{37} - 284 q^{38} + 364 q^{39} + 820 q^{40} - 756 q^{41} - 140 q^{42} + 268 q^{43} - 1824 q^{44} - 296 q^{45} + 184 q^{46} + 1192 q^{47} - 3458 q^{48} + 1666 q^{49} - 320 q^{50} + 336 q^{51} - 3182 q^{52} - 144 q^{53} - 2454 q^{54} + 1280 q^{55} - 1944 q^{57} + 214 q^{58} + 472 q^{59} - 148 q^{60} - 1984 q^{61} + 1374 q^{62} + 3126 q^{64} - 2536 q^{65} - 4084 q^{66} - 548 q^{67} - 3180 q^{68} + 784 q^{70} + 1292 q^{71} - 1474 q^{72} + 900 q^{73} - 6856 q^{74} - 620 q^{75} + 5160 q^{76} + 840 q^{77} + 398 q^{78} + 2480 q^{79} - 6712 q^{80} + 4802 q^{81} - 1094 q^{82} + 268 q^{83} - 1792 q^{84} - 768 q^{85} - 2116 q^{86} + 44 q^{87} + 1004 q^{88} - 1284 q^{89} - 2752 q^{90} + 504 q^{91} + 1104 q^{92} + 2968 q^{93} + 1846 q^{94} + 3024 q^{95} - 4062 q^{96} - 2532 q^{97} - 884 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(161))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 23
161.4.a.a 161.a 1.a $5$ $9.499$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-4\) \(-11\) \(-4\) \(35\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-2-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
161.4.a.b 161.a 1.a $8$ $9.499$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-3\) \(-24\) \(-56\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(3+\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
161.4.a.c 161.a 1.a $9$ $9.499$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(9\) \(-4\) \(-63\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{4})q^{3}+(5+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
161.4.a.d 161.a 1.a $12$ $9.499$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(1\) \(16\) \(84\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(6+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(161))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(161)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)