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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(483))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7 23
483.2.a.a \(1\) \(3.857\) \(\Q\) None \(2\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots\)
483.2.a.b \(1\) \(3.857\) \(\Q\) None \(2\) \(1\) \(4\) \(-1\) \(-\) \(+\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots\)
483.2.a.c \(2\) \(3.857\) \(\Q(\sqrt{5}) \) None \(-3\) \(2\) \(-5\) \(2\) \(-\) \(-\) \(+\) \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-2+\cdots)q^{5}+\cdots\)
483.2.a.d \(2\) \(3.857\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(1\) \(-2\) \(+\) \(+\) \(+\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
483.2.a.e \(2\) \(3.857\) \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(5\) \(2\) \(-\) \(-\) \(-\) \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(3-\beta )q^{5}+\cdots\)
483.2.a.f \(2\) \(3.857\) \(\Q(\sqrt{13}) \) None \(-1\) \(2\) \(-5\) \(-2\) \(-\) \(+\) \(-\) \(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}+(-3+\beta )q^{5}+\cdots\)
483.2.a.g \(2\) \(3.857\) \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(-3\) \(2\) \(+\) \(-\) \(-\) \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
483.2.a.h \(3\) \(3.857\) 3.3.837.1 None \(0\) \(3\) \(3\) \(-3\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
483.2.a.i \(4\) \(3.857\) 4.4.24197.1 None \(0\) \(-4\) \(5\) \(4\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
483.2.a.j \(4\) \(3.857\) 4.4.15317.1 None \(2\) \(-4\) \(5\) \(-4\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)

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

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