Properties

Label 261.2.a
Level $261$
Weight $2$
Character orbit 261.a
Rep. character $\chi_{261}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $5$
Sturm bound $60$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 261.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(60\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(261))\).

Total New Old
Modular forms 34 11 23
Cusp forms 27 11 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.

\(3\)\(29\)FrickeDim
\(+\)\(+\)$+$\(2\)
\(+\)\(-\)$-$\(2\)
\(-\)\(+\)$-$\(5\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(7\)

Trace form

\( 11 q - q^{2} + 5 q^{4} + 3 q^{8} + O(q^{10}) \) \( 11 q - q^{2} + 5 q^{4} + 3 q^{8} - 4 q^{10} + 2 q^{11} - 4 q^{13} + 4 q^{14} - 7 q^{16} - 6 q^{17} + 24 q^{20} - 6 q^{22} + 7 q^{25} - 8 q^{26} + 4 q^{28} - 3 q^{29} + 6 q^{31} - 5 q^{32} + 22 q^{34} + 4 q^{35} - 10 q^{37} - 8 q^{38} - 16 q^{40} - 10 q^{41} - 2 q^{43} + 14 q^{44} - 12 q^{46} + 14 q^{47} - 5 q^{49} - 53 q^{50} - 28 q^{52} - 28 q^{53} + 14 q^{55} - 32 q^{56} + q^{58} + 16 q^{59} - 14 q^{61} + 46 q^{62} - 7 q^{64} - 2 q^{65} + 20 q^{67} - 38 q^{68} - 8 q^{70} + 32 q^{71} + 10 q^{73} + 10 q^{74} + 24 q^{76} + 8 q^{77} - 2 q^{79} + 32 q^{80} - 18 q^{82} + 16 q^{83} - 24 q^{85} - 26 q^{86} + 10 q^{88} + 6 q^{89} - 32 q^{91} - 40 q^{92} - 26 q^{94} + 44 q^{95} + 34 q^{97} + 11 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(261))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 29
261.2.a.a 261.a 1.a $2$ $2.084$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-4\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}-2q^{5}+(-1+\cdots)q^{7}+\cdots\)
261.2.a.b 261.a 1.a $2$ $2.084$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-2\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(-2+2\beta )q^{5}+\cdots\)
261.2.a.c 261.a 1.a $2$ $2.084$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(4\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+2q^{5}+(-1+\cdots)q^{7}+\cdots\)
261.2.a.d 261.a 1.a $2$ $2.084$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}-2\beta q^{7}+\cdots\)
261.2.a.e 261.a 1.a $3$ $2.084$ 3.3.229.1 None \(-2\) \(0\) \(0\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+2\beta _{1}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(261))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(261)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 2}\)