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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 47
141.2.a.a \(1\) \(1.126\) \(\Q\) None \(-2\) \(1\) \(-3\) \(-3\) \(-\) \(-\) \(q-2q^{2}+q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots\)
141.2.a.b \(1\) \(1.126\) \(\Q\) None \(-1\) \(-1\) \(0\) \(4\) \(+\) \(-\) \(q-q^{2}-q^{3}-q^{4}+q^{6}+4q^{7}+3q^{8}+\cdots\)
141.2.a.c \(1\) \(1.126\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(-\) \(+\) \(q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}+3q^{8}+\cdots\)
141.2.a.d \(1\) \(1.126\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) \(+\) \(+\) \(q-q^{3}-2q^{4}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
141.2.a.e \(1\) \(1.126\) \(\Q\) None \(2\) \(1\) \(-1\) \(-3\) \(-\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-3q^{7}+\cdots\)
141.2.a.f \(2\) \(1.126\) \(\Q(\sqrt{17}) \) None \(-1\) \(-2\) \(1\) \(1\) \(+\) \(-\) \(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+(1-\beta )q^{5}+\cdots\)

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

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