Properties

Label 155.2.a
Level $155$
Weight $2$
Character orbit 155.a
Rep. character $\chi_{155}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $5$
Sturm bound $32$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 155 = 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 155.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(32\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(155))\).

Total New Old
Modular forms 18 11 7
Cusp forms 15 11 4
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.

\(5\)\(31\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(9\)

Trace form

\( 11 q - 3 q^{2} + 13 q^{4} - q^{5} + 4 q^{6} + 4 q^{7} - 3 q^{8} + 3 q^{9} + O(q^{10}) \) \( 11 q - 3 q^{2} + 13 q^{4} - q^{5} + 4 q^{6} + 4 q^{7} - 3 q^{8} + 3 q^{9} + q^{10} - 8 q^{11} - 4 q^{12} + 14 q^{13} - 8 q^{14} + 13 q^{16} + 2 q^{17} - 11 q^{18} + q^{20} + 12 q^{21} - 24 q^{22} + 12 q^{23} - 24 q^{24} + 11 q^{25} + 2 q^{26} + 12 q^{27} - 16 q^{28} - 18 q^{29} - 8 q^{30} + q^{31} - 19 q^{32} - 12 q^{33} + 2 q^{34} - 4 q^{35} - 31 q^{36} + 2 q^{37} - 16 q^{38} - 4 q^{39} + 9 q^{40} - 10 q^{41} - 28 q^{42} + 20 q^{43} + 4 q^{44} - 9 q^{45} - 20 q^{46} - 24 q^{47} - 16 q^{48} + 11 q^{49} - 3 q^{50} - 8 q^{51} + 42 q^{52} + 26 q^{53} + 28 q^{54} + 4 q^{55} - 16 q^{56} + 8 q^{57} + 18 q^{58} + 12 q^{59} + 12 q^{60} + 34 q^{61} - 5 q^{62} - 16 q^{63} + 29 q^{64} - 6 q^{65} + 8 q^{66} - 8 q^{67} + 42 q^{68} + 12 q^{69} - 16 q^{70} - 12 q^{71} + 9 q^{72} + 14 q^{73} - 2 q^{74} + 4 q^{76} + 28 q^{77} + 24 q^{78} - 28 q^{79} - 15 q^{80} + 7 q^{81} + 54 q^{82} - 32 q^{83} + 32 q^{84} + 6 q^{85} + 12 q^{86} + 12 q^{87} - 36 q^{88} + 2 q^{89} - 7 q^{90} - 16 q^{91} + 4 q^{92} + 24 q^{94} - 16 q^{95} + 24 q^{96} + 6 q^{97} + 53 q^{98} - 52 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(155))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 31
155.2.a.a 155.a 1.a $1$ $1.238$ \(\Q\) None \(-2\) \(-1\) \(1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
155.2.a.b 155.a 1.a $1$ $1.238$ \(\Q\) None \(-1\) \(2\) \(-1\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}-q^{4}-q^{5}-2q^{6}+4q^{7}+\cdots\)
155.2.a.c 155.a 1.a $1$ $1.238$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}-2q^{9}-4q^{11}+\cdots\)
155.2.a.d 155.a 1.a $4$ $1.238$ 4.4.20308.1 None \(-1\) \(-1\) \(-4\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots\)
155.2.a.e 155.a 1.a $4$ $1.238$ 4.4.8468.1 None \(1\) \(1\) \(4\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(155))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(155)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)