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Properties

Label 867.2.a
Level $867$
Weight $2$
Character orbit 867.a
Rep. character $\chi_{867}(1,\cdot)$
Character field $\Q$
Dimension $45$
Newform subspaces $16$
Sturm bound $204$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 867 = 3 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 867.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(204\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(867))\).

Total New Old
Modular forms 120 45 75
Cusp forms 85 45 40
Eisenstein series 35 0 35

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

\(3\)\(17\)FrickeDim
\(+\)\(+\)$+$\(10\)
\(+\)\(-\)$-$\(12\)
\(-\)\(+\)$-$\(16\)
\(-\)\(-\)$+$\(7\)
Plus space\(+\)\(17\)
Minus space\(-\)\(28\)

Trace form

\( 45 q + q^{2} + q^{3} + 45 q^{4} - 6 q^{5} - q^{6} + 4 q^{7} + 9 q^{8} + 45 q^{9} + O(q^{10}) \) \( 45 q + q^{2} + q^{3} + 45 q^{4} - 6 q^{5} - q^{6} + 4 q^{7} + 9 q^{8} + 45 q^{9} + 10 q^{10} + 4 q^{11} + 7 q^{12} - 6 q^{13} - 2 q^{15} + 41 q^{16} + q^{18} - 4 q^{19} - 10 q^{20} + 4 q^{21} + 8 q^{22} - 9 q^{24} + 39 q^{25} - 6 q^{26} + q^{27} - 8 q^{28} - 6 q^{29} - 10 q^{30} + 9 q^{32} + 4 q^{35} + 45 q^{36} + 6 q^{37} - 32 q^{38} + 6 q^{39} + 22 q^{40} + 6 q^{41} - 12 q^{44} - 6 q^{45} + 4 q^{46} + 16 q^{47} - q^{48} + 49 q^{49} + 19 q^{50} - 14 q^{52} - 6 q^{53} - q^{54} - 8 q^{55} + 4 q^{57} - 34 q^{58} - 24 q^{59} + 14 q^{60} - 18 q^{61} + 16 q^{62} + 4 q^{63} + 37 q^{64} + 4 q^{65} - 20 q^{66} - 16 q^{67} - 20 q^{69} - 20 q^{70} - 16 q^{71} + 9 q^{72} + 6 q^{73} - 18 q^{74} - q^{75} - 4 q^{76} - 16 q^{77} + 6 q^{78} + 4 q^{79} - 42 q^{80} + 45 q^{81} - 10 q^{82} + 8 q^{83} - 20 q^{84} + 16 q^{86} - 14 q^{87} + 4 q^{88} - 18 q^{89} + 10 q^{90} - 4 q^{91} + 32 q^{92} - 4 q^{93} - 44 q^{94} + 24 q^{95} - 9 q^{96} + 30 q^{97} - 43 q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(867))\) 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 17
867.2.a.a 867.a 1.a $1$ $6.923$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-4q^{7}+3q^{8}+\cdots\)
867.2.a.b 867.a 1.a $1$ $6.923$ \(\Q\) None \(-1\) \(1\) \(0\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+4q^{7}+3q^{8}+\cdots\)
867.2.a.c 867.a 1.a $1$ $6.923$ \(\Q\) None \(0\) \(-1\) \(-3\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-3q^{5}+4q^{7}+q^{9}+3q^{11}+\cdots\)
867.2.a.d 867.a 1.a $1$ $6.923$ \(\Q\) None \(2\) \(-1\) \(-3\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots\)
867.2.a.e 867.a 1.a $1$ $6.923$ \(\Q\) None \(2\) \(1\) \(3\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+3q^{5}+2q^{6}+\cdots\)
867.2.a.f 867.a 1.a $2$ $6.923$ \(\Q(\sqrt{17}) \) None \(-1\) \(2\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
867.2.a.g 867.a 1.a $2$ $6.923$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(-6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+2\beta q^{5}+\cdots\)
867.2.a.h 867.a 1.a $2$ $6.923$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}-2\beta q^{5}+\cdots\)
867.2.a.i 867.a 1.a $3$ $6.923$ \(\Q(\zeta_{18})^+\) None \(-3\) \(-3\) \(3\) \(3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
867.2.a.j 867.a 1.a $3$ $6.923$ \(\Q(\zeta_{18})^+\) None \(-3\) \(3\) \(-3\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
867.2.a.k 867.a 1.a $4$ $6.923$ 4.4.7232.1 None \(-2\) \(-4\) \(-6\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{3})q^{2}-q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
867.2.a.l 867.a 1.a $4$ $6.923$ 4.4.7232.1 None \(-2\) \(4\) \(6\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{3})q^{2}+q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
867.2.a.m 867.a 1.a $4$ $6.923$ \(\Q(\zeta_{16})^+\) None \(0\) \(-4\) \(4\) \(8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\beta _{3})q^{5}+\cdots\)
867.2.a.n 867.a 1.a $4$ $6.923$ \(\Q(\zeta_{16})^+\) None \(0\) \(4\) \(-4\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
867.2.a.o 867.a 1.a $6$ $6.923$ 6.6.3418281.1 None \(3\) \(-6\) \(3\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
867.2.a.p 867.a 1.a $6$ $6.923$ 6.6.3418281.1 None \(3\) \(6\) \(-3\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(867))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(867)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 2}\)