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Properties

Label 174.2.a
Level $174$
Weight $2$
Character orbit 174.a
Rep. character $\chi_{174}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $5$
Sturm bound $60$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 174 = 2 \cdot 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 174.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(60\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(174))\).

Total New Old
Modular forms 34 5 29
Cusp forms 27 5 22
Eisenstein series 7 0 7

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

\(2\)\(3\)\(29\)FrickeDim
\(+\)\(+\)\(-\)$-$\(1\)
\(+\)\(-\)\(+\)$-$\(2\)
\(-\)\(+\)\(+\)$-$\(1\)
\(-\)\(-\)\(-\)$-$\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(5\)

Trace form

\( 5 q - q^{2} + q^{3} + 5 q^{4} + 2 q^{5} - q^{6} + 4 q^{7} - q^{8} + 5 q^{9} + O(q^{10}) \) \( 5 q - q^{2} + q^{3} + 5 q^{4} + 2 q^{5} - q^{6} + 4 q^{7} - q^{8} + 5 q^{9} - 2 q^{10} + 12 q^{11} + q^{12} - 2 q^{13} - 6 q^{15} + 5 q^{16} - 2 q^{17} - q^{18} + 4 q^{19} + 2 q^{20} + 8 q^{21} - 4 q^{22} - 8 q^{23} - q^{24} - q^{25} - 6 q^{26} + q^{27} + 4 q^{28} - q^{29} + 2 q^{30} - 12 q^{31} - q^{32} - 12 q^{33} - 18 q^{34} - 24 q^{35} + 5 q^{36} - 14 q^{37} - 12 q^{38} + 6 q^{39} - 2 q^{40} - 10 q^{41} - 8 q^{42} - 12 q^{43} + 12 q^{44} + 2 q^{45} + 8 q^{46} - 8 q^{47} + q^{48} + q^{49} - 15 q^{50} - 2 q^{51} - 2 q^{52} - 6 q^{53} - q^{54} + q^{58} - 6 q^{60} + 10 q^{61} + 20 q^{62} + 4 q^{63} + 5 q^{64} + 20 q^{65} - 4 q^{66} + 4 q^{67} - 2 q^{68} + 24 q^{70} + 16 q^{71} - q^{72} - 6 q^{73} + 6 q^{74} - q^{75} + 4 q^{76} + 16 q^{77} + 2 q^{78} + 20 q^{79} + 2 q^{80} + 5 q^{81} + 6 q^{82} + 16 q^{83} + 8 q^{84} + 4 q^{85} + 20 q^{86} - q^{87} - 4 q^{88} + 14 q^{89} - 2 q^{90} - 24 q^{91} - 8 q^{92} + 4 q^{93} - 4 q^{94} + 24 q^{95} - q^{96} + 18 q^{97} - 25 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(174))\) 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 3 29
174.2.a.a 174.a 1.a $1$ $1.389$ \(\Q\) None \(-1\) \(-1\) \(3\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-3q^{7}+\cdots\)
174.2.a.b 174.a 1.a $1$ $1.389$ \(\Q\) None \(-1\) \(1\) \(-3\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}+5q^{7}+\cdots\)
174.2.a.c 174.a 1.a $1$ $1.389$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
174.2.a.d 174.a 1.a $1$ $1.389$ \(\Q\) None \(1\) \(-1\) \(1\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
174.2.a.e 174.a 1.a $1$ $1.389$ \(\Q\) None \(1\) \(1\) \(-1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(174))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(174)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 2}\)