Properties

Label 141.2.a
Level $141$
Weight $2$
Character orbit 141.a
Rep. character $\chi_{141}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $6$
Sturm bound $32$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 141 = 3 \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 141.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(141))\).

Total New Old
Modular forms 18 7 11
Cusp forms 15 7 8
Eisenstein series 3 0 3

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

\(3\)\(47\)FrickeDim
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(3\)
\(-\)\(+\)$-$\(2\)
\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(5\)

Trace form

\( 7 q - 3 q^{2} - q^{3} + 5 q^{4} - 2 q^{5} + q^{6} - 4 q^{7} - 3 q^{8} + 7 q^{9} + O(q^{10}) \) \( 7 q - 3 q^{2} - q^{3} + 5 q^{4} - 2 q^{5} + q^{6} - 4 q^{7} - 3 q^{8} + 7 q^{9} + 10 q^{10} + 4 q^{11} + q^{12} - 6 q^{13} + 4 q^{14} - 2 q^{15} - 3 q^{16} + 2 q^{17} - 3 q^{18} + 8 q^{19} - 14 q^{20} - 8 q^{21} - 4 q^{22} + 16 q^{23} + 9 q^{24} - 11 q^{25} - 26 q^{26} - q^{27} - 16 q^{28} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 19 q^{32} - 4 q^{33} + 2 q^{34} + 24 q^{35} + 5 q^{36} - 10 q^{37} + 16 q^{38} + 2 q^{39} + 10 q^{40} + 2 q^{41} - 4 q^{42} + 20 q^{44} - 2 q^{45} - 40 q^{46} + q^{47} - 15 q^{48} + 3 q^{49} - q^{50} - 6 q^{51} + 6 q^{52} + 6 q^{53} + q^{54} + 20 q^{55} + 16 q^{56} - 8 q^{57} + 18 q^{58} - 6 q^{60} + 10 q^{61} + 20 q^{62} - 4 q^{63} - 3 q^{64} - 24 q^{65} + 20 q^{66} + 8 q^{67} + 2 q^{68} + 8 q^{69} - 8 q^{70} - 8 q^{71} - 3 q^{72} - 18 q^{73} - 14 q^{74} + 9 q^{75} + 40 q^{76} + 16 q^{77} + 14 q^{78} - 12 q^{79} - 14 q^{80} + 7 q^{81} - 2 q^{82} - 8 q^{83} - 8 q^{84} - 4 q^{85} - 16 q^{86} + 6 q^{87} - 28 q^{88} + 22 q^{89} + 10 q^{90} + 16 q^{91} + 32 q^{92} - 20 q^{93} - 5 q^{94} + 24 q^{95} + 9 q^{96} - 30 q^{97} + 9 q^{98} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(141))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 47
141.2.a.a 141.a 1.a $1$ $1.126$ \(\Q\) None \(-2\) \(1\) \(-3\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots\)
141.2.a.b 141.a 1.a $1$ $1.126$ \(\Q\) None \(-1\) \(-1\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+4q^{7}+3q^{8}+\cdots\)
141.2.a.c 141.a 1.a $1$ $1.126$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}+3q^{8}+\cdots\)
141.2.a.d 141.a 1.a $1$ $1.126$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
141.2.a.e 141.a 1.a $1$ $1.126$ \(\Q\) None \(2\) \(1\) \(-1\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-3q^{7}+\cdots\)
141.2.a.f 141.a 1.a $2$ $1.126$ \(\Q(\sqrt{17}) \) None \(-1\) \(-2\) \(1\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+(1-\beta )q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(141))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(141)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 2}\)