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Properties

Label 202.2.a
Level $202$
Weight $2$
Character orbit 202.a
Rep. character $\chi_{202}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $3$
Sturm bound $51$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 202 = 2 \cdot 101 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 202.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(51\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(202))\).

Total New Old
Modular forms 27 8 19
Cusp forms 24 8 16
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.

\(2\)\(101\)FrickeDim
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(4\)
Plus space\(+\)\(3\)
Minus space\(-\)\(5\)

Trace form

\( 8 q - 4 q^{3} + 8 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{3} + 8 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 2 q^{13} + 4 q^{14} - 12 q^{15} + 8 q^{16} + 8 q^{18} - 18 q^{19} + 2 q^{20} - 12 q^{21} + 6 q^{22} - 4 q^{23} + 2 q^{24} + 2 q^{25} + 4 q^{26} - 28 q^{27} + 4 q^{29} + 4 q^{31} + 8 q^{33} + 8 q^{34} - 12 q^{35} + 2 q^{36} - 6 q^{37} - 8 q^{38} + 8 q^{39} + 4 q^{40} - 12 q^{42} - 14 q^{43} - 4 q^{44} + 18 q^{45} + 8 q^{46} - 4 q^{47} - 4 q^{48} + 12 q^{49} - 8 q^{50} - 12 q^{51} - 2 q^{52} + 24 q^{53} - 16 q^{54} + 8 q^{55} + 4 q^{56} + 20 q^{57} + 14 q^{58} + 12 q^{59} - 12 q^{60} - 20 q^{62} + 24 q^{63} + 8 q^{64} + 12 q^{65} - 16 q^{66} - 36 q^{67} + 28 q^{69} - 4 q^{70} - 16 q^{71} + 8 q^{72} + 4 q^{74} - 8 q^{75} - 18 q^{76} + 12 q^{77} - 28 q^{78} - 8 q^{79} + 2 q^{80} + 40 q^{81} - 4 q^{82} + 28 q^{83} - 12 q^{84} + 16 q^{85} + 8 q^{86} + 20 q^{87} + 6 q^{88} - 12 q^{89} - 24 q^{90} - 52 q^{91} - 4 q^{92} - 4 q^{93} - 4 q^{94} + 20 q^{95} + 2 q^{96} + 32 q^{97} - 24 q^{98} - 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(202))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 101
202.2.a.a 202.a 1.a $1$ $1.613$ \(\Q\) None 202.2.a.a \(-1\) \(0\) \(2\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
202.2.a.b 202.a 1.a $3$ $1.613$ \(\Q(\zeta_{18})^+\) None 202.2.a.b \(-3\) \(-3\) \(-3\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
202.2.a.c 202.a 1.a $4$ $1.613$ 4.4.10273.1 None 202.2.a.c \(4\) \(-1\) \(3\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+(1-\beta _{3})q^{5}+\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(202))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(202)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(101))\)\(^{\oplus 2}\)