Properties

Label 862.2.a
Level $862$
Weight $2$
Character orbit 862.a
Rep. character $\chi_{862}(1,\cdot)$
Character field $\Q$
Dimension $35$
Newform subspaces $11$
Sturm bound $216$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 862 = 2 \cdot 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 862.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(216\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(862))\).

Total New Old
Modular forms 110 35 75
Cusp forms 107 35 72
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.

\(2\)\(431\)FrickeDim
\(+\)\(+\)$+$\(8\)
\(+\)\(-\)$-$\(10\)
\(-\)\(+\)$-$\(9\)
\(-\)\(-\)$+$\(8\)
Plus space\(+\)\(16\)
Minus space\(-\)\(19\)

Trace form

\( 35 q - q^{2} - 4 q^{3} + 35 q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} + 31 q^{9} + O(q^{10}) \) \( 35 q - q^{2} - 4 q^{3} + 35 q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} + 31 q^{9} - 6 q^{10} - 4 q^{12} + 35 q^{16} - 2 q^{17} + 3 q^{18} - 8 q^{19} - 6 q^{20} + 4 q^{23} - 4 q^{24} + 21 q^{25} - 4 q^{27} - 8 q^{28} - 2 q^{29} + 4 q^{30} - 28 q^{31} - q^{32} + 12 q^{33} - 14 q^{34} - 4 q^{35} + 31 q^{36} - 24 q^{37} - 4 q^{38} + 16 q^{39} - 6 q^{40} - 6 q^{41} - 8 q^{42} - 18 q^{43} - 42 q^{45} - 4 q^{46} - 20 q^{47} - 4 q^{48} + 7 q^{49} - 15 q^{50} + 28 q^{51} + 22 q^{53} - 40 q^{54} - 12 q^{55} - 20 q^{57} - 22 q^{58} - 18 q^{61} - 4 q^{62} - 4 q^{63} + 35 q^{64} - 12 q^{65} - 8 q^{66} - 14 q^{67} - 2 q^{68} + 16 q^{69} - 28 q^{70} - 12 q^{71} + 3 q^{72} - 42 q^{73} + 4 q^{74} + 4 q^{75} - 8 q^{76} - 12 q^{77} + 16 q^{78} - 4 q^{79} - 6 q^{80} + 75 q^{81} - 26 q^{82} + 38 q^{83} - 4 q^{85} + 2 q^{86} + 24 q^{87} + 6 q^{89} + 14 q^{90} - 24 q^{91} + 4 q^{92} + 36 q^{93} - 12 q^{94} + 52 q^{95} - 4 q^{96} - 22 q^{97} + 23 q^{98} + 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(862))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 431
862.2.a.a 862.a 1.a $1$ $6.883$ \(\Q\) None \(-1\) \(-3\) \(-1\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}-2q^{7}+\cdots\)
862.2.a.b 862.a 1.a $1$ $6.883$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
862.2.a.c 862.a 1.a $1$ $6.883$ \(\Q\) None \(1\) \(-1\) \(-3\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+2q^{7}+\cdots\)
862.2.a.d 862.a 1.a $1$ $6.883$ \(\Q\) None \(1\) \(-1\) \(1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
862.2.a.e 862.a 1.a $1$ $6.883$ \(\Q\) None \(1\) \(0\) \(2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+4q^{7}+q^{8}-3q^{9}+\cdots\)
862.2.a.f 862.a 1.a $1$ $6.883$ \(\Q\) None \(1\) \(1\) \(-3\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+2q^{7}+\cdots\)
862.2.a.g 862.a 1.a $2$ $6.883$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
862.2.a.h 862.a 1.a $5$ $6.883$ 5.5.181057.1 None \(5\) \(5\) \(3\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{2})q^{3}+q^{4}+(1+\beta _{3})q^{5}+\cdots\)
862.2.a.i 862.a 1.a $6$ $6.883$ 6.6.11017801.1 None \(-6\) \(-2\) \(-2\) \(3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{2}+\beta _{4}-\beta _{5})q^{5}+\cdots\)
862.2.a.j 862.a 1.a $6$ $6.883$ 6.6.9783113.1 None \(6\) \(-8\) \(-8\) \(-9\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{2}+\beta _{4})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots\)
862.2.a.k 862.a 1.a $10$ $6.883$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(4\) \(4\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{5}q^{3}+q^{4}+(-\beta _{7}-\beta _{9})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(862))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(862)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(431))\)\(^{\oplus 2}\)