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Properties

Label 154.2.a
Level $154$
Weight $2$
Character orbit 154.a
Rep. character $\chi_{154}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(154))\).

Total New Old
Modular forms 28 5 23
Cusp forms 21 5 16
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.

\(2\)\(7\)\(11\)FrickeDim
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(-\)$-$\(1\)
\(-\)\(+\)\(+\)$-$\(1\)
\(-\)\(-\)\(-\)$-$\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(4\)

Trace form

\( 5 q + q^{2} + 5 q^{4} + 2 q^{5} - 4 q^{6} - q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 5 q + q^{2} + 5 q^{4} + 2 q^{5} - 4 q^{6} - q^{7} + q^{8} + q^{9} + 6 q^{10} + q^{11} - 2 q^{13} + 3 q^{14} - 8 q^{15} + 5 q^{16} - 6 q^{17} + 5 q^{18} - 12 q^{19} + 2 q^{20} - 4 q^{21} + q^{22} + 8 q^{23} - 4 q^{24} + 11 q^{25} + 2 q^{26} - 24 q^{27} - q^{28} - 2 q^{29} - 16 q^{30} - 16 q^{31} + q^{32} + 2 q^{34} + 2 q^{35} + q^{36} - 2 q^{37} - 8 q^{38} - 16 q^{39} + 6 q^{40} + 18 q^{41} - 20 q^{43} + q^{44} + 34 q^{45} - 8 q^{46} + 16 q^{47} + 5 q^{49} - 9 q^{50} + 24 q^{51} - 2 q^{52} + 6 q^{53} - 16 q^{54} + 6 q^{55} + 3 q^{56} + 8 q^{57} - 2 q^{58} + 8 q^{59} - 8 q^{60} - 18 q^{61} + 8 q^{62} + 11 q^{63} + 5 q^{64} - 4 q^{65} - 4 q^{66} - 20 q^{67} - 6 q^{68} - 2 q^{70} + 8 q^{71} + 5 q^{72} + 2 q^{73} - 10 q^{74} - 24 q^{75} - 12 q^{76} + 3 q^{77} + 16 q^{79} + 2 q^{80} + 29 q^{81} + 10 q^{82} - 4 q^{83} - 4 q^{84} - 4 q^{85} + 4 q^{86} + 24 q^{87} + q^{88} + 18 q^{89} + 6 q^{90} - 2 q^{91} + 8 q^{92} - 24 q^{93} - 8 q^{94} + 32 q^{95} - 4 q^{96} + 18 q^{97} + q^{98} + 13 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(154))\) 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 7 11
154.2.a.a 154.a 1.a $1$ $1.230$ \(\Q\) None \(-1\) \(0\) \(-4\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}-3q^{9}+\cdots\)
154.2.a.b 154.a 1.a $1$ $1.230$ \(\Q\) None \(-1\) \(2\) \(2\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}-q^{7}+\cdots\)
154.2.a.c 154.a 1.a $1$ $1.230$ \(\Q\) None \(1\) \(0\) \(2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
154.2.a.d 154.a 1.a $2$ $1.230$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(154))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(154)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 2}\)