Properties

Label 483.2.a
Level $483$
Weight $2$
Character orbit 483.a
Rep. character $\chi_{483}(1,\cdot)$
Character field $\Q$
Dimension $23$
Newform subspaces $10$
Sturm bound $128$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(128\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(483))\).

Total New Old
Modular forms 68 23 45
Cusp forms 61 23 38
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.

\(3\)\(7\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(8\)
Minus space\(-\)\(15\)

Trace form

\( 23 q + q^{2} - q^{3} + 21 q^{4} + 10 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 23 q^{9} + O(q^{10}) \) \( 23 q + q^{2} - q^{3} + 21 q^{4} + 10 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 23 q^{9} + 6 q^{10} - 12 q^{11} + 9 q^{12} + 2 q^{13} - 3 q^{14} - 6 q^{15} + 21 q^{16} + 14 q^{17} + q^{18} - 20 q^{19} - 2 q^{20} - q^{21} - 20 q^{22} - q^{23} - 15 q^{24} + 33 q^{25} - 18 q^{26} - q^{27} - 7 q^{28} + 2 q^{29} - 2 q^{30} - 24 q^{31} + 5 q^{32} - 4 q^{33} + 10 q^{34} - 6 q^{35} + 21 q^{36} - 14 q^{37} + 36 q^{38} + 2 q^{39} + 38 q^{40} + 14 q^{41} - 3 q^{42} + 4 q^{43} + 12 q^{44} + 10 q^{45} + 5 q^{46} - 24 q^{47} + q^{48} + 23 q^{49} + 7 q^{50} - 10 q^{51} - 2 q^{52} - 6 q^{53} - 3 q^{54} + 16 q^{55} - 15 q^{56} - 4 q^{57} + 6 q^{58} - 20 q^{59} - 18 q^{60} + 2 q^{61} - 24 q^{62} - q^{63} - 19 q^{64} + 52 q^{65} - 20 q^{66} - 20 q^{67} + 2 q^{68} - q^{69} + 14 q^{70} - 16 q^{71} - 3 q^{72} + 22 q^{73} - 18 q^{74} + 17 q^{75} - 100 q^{76} + 4 q^{77} + 30 q^{78} - 48 q^{79} - 42 q^{80} + 23 q^{81} - 30 q^{82} - 12 q^{83} - 7 q^{84} - 4 q^{85} - 84 q^{86} - 6 q^{87} - 28 q^{88} + 46 q^{89} + 6 q^{90} - 14 q^{91} - 7 q^{92} - 24 q^{93} + 8 q^{94} - 24 q^{95} - 23 q^{96} - 26 q^{97} + q^{98} - 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(483))\) 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 7 23
483.2.a.a 483.a 1.a $1$ $3.857$ \(\Q\) None \(2\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots\)
483.2.a.b 483.a 1.a $1$ $3.857$ \(\Q\) None \(2\) \(1\) \(4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots\)
483.2.a.c 483.a 1.a $2$ $3.857$ \(\Q(\sqrt{5}) \) None \(-3\) \(2\) \(-5\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-2+\cdots)q^{5}+\cdots\)
483.2.a.d 483.a 1.a $2$ $3.857$ \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
483.2.a.e 483.a 1.a $2$ $3.857$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(5\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(3-\beta )q^{5}+\cdots\)
483.2.a.f 483.a 1.a $2$ $3.857$ \(\Q(\sqrt{13}) \) None \(-1\) \(2\) \(-5\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}+(-3+\beta )q^{5}+\cdots\)
483.2.a.g 483.a 1.a $2$ $3.857$ \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(-3\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
483.2.a.h 483.a 1.a $3$ $3.857$ 3.3.837.1 None \(0\) \(3\) \(3\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
483.2.a.i 483.a 1.a $4$ $3.857$ 4.4.24197.1 None \(0\) \(-4\) \(5\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
483.2.a.j 483.a 1.a $4$ $3.857$ 4.4.15317.1 None \(2\) \(-4\) \(5\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(483))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(483)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 2}\)