Properties

Label 723.2.a
Level $723$
Weight $2$
Character orbit 723.a
Rep. character $\chi_{723}(1,\cdot)$
Character field $\Q$
Dimension $41$
Newform subspaces $7$
Sturm bound $161$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 723 = 3 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 723.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(161\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(723))\).

Total New Old
Modular forms 82 41 41
Cusp forms 79 41 38
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.

\(3\)\(241\)FrickeDim
\(+\)\(+\)$+$\(11\)
\(+\)\(-\)$-$\(9\)
\(-\)\(+\)$-$\(15\)
\(-\)\(-\)$+$\(6\)
Plus space\(+\)\(17\)
Minus space\(-\)\(24\)

Trace form

\( 41 q - q^{2} + q^{3} + 43 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{8} + 41 q^{9} + O(q^{10}) \) \( 41 q - q^{2} + q^{3} + 43 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{8} + 41 q^{9} - 2 q^{10} - 4 q^{11} - q^{12} + 2 q^{13} - 16 q^{14} + 2 q^{15} + 35 q^{16} + 2 q^{17} - q^{18} + 8 q^{19} - 2 q^{20} + 4 q^{21} - 12 q^{23} + 15 q^{24} + 55 q^{25} - 2 q^{26} + q^{27} - 20 q^{28} - 2 q^{29} - 14 q^{30} - 29 q^{32} + 4 q^{33} - 14 q^{34} - 32 q^{35} + 43 q^{36} - 10 q^{37} - 32 q^{38} + 6 q^{39} + 26 q^{40} + 6 q^{41} + 12 q^{42} - 24 q^{43} - 32 q^{44} + 2 q^{45} - 12 q^{46} - 36 q^{47} - q^{48} + 61 q^{49} - 15 q^{50} - 6 q^{51} - 10 q^{52} - 2 q^{53} + 3 q^{54} - 44 q^{55} - 68 q^{56} + 34 q^{58} - 12 q^{59} + 26 q^{60} + 6 q^{61} + 8 q^{62} + 31 q^{64} + 72 q^{65} - 12 q^{66} - 20 q^{67} + 50 q^{68} - 8 q^{69} - 24 q^{70} - 32 q^{71} - 9 q^{72} + 14 q^{73} + 30 q^{74} - 9 q^{75} + 48 q^{76} - 48 q^{77} - 6 q^{78} + 8 q^{79} + 2 q^{80} + 41 q^{81} - 70 q^{82} + 20 q^{83} - 20 q^{84} - 12 q^{85} - 32 q^{86} + 2 q^{87} - 20 q^{88} + 6 q^{89} - 2 q^{90} + 8 q^{91} - 76 q^{92} - 4 q^{93} - 4 q^{94} + 32 q^{95} + 43 q^{96} + 14 q^{97} + 39 q^{98} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(723))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 241
723.2.a.a 723.a 1.a $1$ $5.773$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots\)
723.2.a.b 723.a 1.a $1$ $5.773$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-2q^{7}+q^{9}-q^{11}-2q^{12}+\cdots\)
723.2.a.c 723.a 1.a $2$ $5.773$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(4\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}+(1+\beta )q^{7}+\cdots\)
723.2.a.d 723.a 1.a $5$ $5.773$ 5.5.24217.1 None \(-2\) \(5\) \(-8\) \(-7\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+q^{3}-\beta _{4}q^{4}+\cdots\)
723.2.a.e 723.a 1.a $9$ $5.773$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(3\) \(-9\) \(12\) \(-5\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{8})q^{5}+\cdots\)
723.2.a.f 723.a 1.a $10$ $5.773$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(-10\) \(-10\) \(3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{9}q^{2}-q^{3}+(1+\beta _{7}-\beta _{9})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
723.2.a.g 723.a 1.a $13$ $5.773$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(1\) \(13\) \(6\) \(9\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(723))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(723)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(241))\)\(^{\oplus 2}\)