Properties

Label 483.2.i
Level $483$
Weight $2$
Character orbit 483.i
Rep. character $\chi_{483}(277,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $60$
Newform subspaces $8$
Sturm bound $128$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 8 \)
Sturm bound: \(128\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(483, [\chi])\).

Total New Old
Modular forms 136 60 76
Cusp forms 120 60 60
Eisenstein series 16 0 16

Trace form

\( 60q + 2q^{3} - 32q^{4} - 8q^{6} + 6q^{7} + 24q^{8} - 30q^{9} + O(q^{10}) \) \( 60q + 2q^{3} - 32q^{4} - 8q^{6} + 6q^{7} + 24q^{8} - 30q^{9} - 16q^{10} + 4q^{12} - 4q^{13} - 12q^{14} + 8q^{15} - 52q^{16} - 8q^{17} - 6q^{19} - 16q^{20} - 8q^{21} + 48q^{22} - 46q^{25} + 32q^{26} - 4q^{27} + 28q^{28} + 24q^{29} + 22q^{31} - 24q^{32} - 12q^{33} - 16q^{34} + 4q^{35} + 64q^{36} - 10q^{37} - 20q^{38} + 2q^{39} - 36q^{40} + 8q^{41} + 16q^{42} - 12q^{43} - 16q^{44} - 8q^{47} - 16q^{48} + 50q^{49} - 40q^{50} + 4q^{54} - 48q^{55} - 8q^{56} + 12q^{57} + 24q^{58} - 20q^{59} + 12q^{60} - 16q^{61} + 24q^{62} - 6q^{63} + 200q^{64} + 36q^{65} - 24q^{66} - 10q^{67} - 12q^{68} - 16q^{69} + 16q^{70} + 8q^{71} - 12q^{72} + 18q^{73} - 12q^{74} + 14q^{75} + 24q^{76} + 8q^{77} - 8q^{78} - 10q^{79} + 92q^{80} - 30q^{81} + 24q^{82} + 56q^{83} + 4q^{84} - 72q^{85} - 44q^{86} + 20q^{87} - 80q^{88} + 32q^{90} - 46q^{91} - 6q^{93} - 20q^{94} - 24q^{95} + 4q^{96} + 40q^{97} - 40q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(483, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
483.2.i.a \(2\) \(3.857\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
483.2.i.b \(2\) \(3.857\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(5\) \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
483.2.i.c \(2\) \(3.857\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
483.2.i.d \(2\) \(3.857\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(3\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
483.2.i.e \(4\) \(3.857\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(1\) \(-2\) \(1\) \(10\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
483.2.i.f \(12\) \(3.857\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(6\) \(-3\) \(-2\) \(q+(-\beta _{1}-\beta _{5})q^{2}+\beta _{7}q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots\)
483.2.i.g \(16\) \(3.857\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-1\) \(-8\) \(-5\) \(-2\) \(q+(\beta _{1}-\beta _{5})q^{2}+(-1-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
483.2.i.h \(20\) \(3.857\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-3\) \(10\) \(5\) \(0\) \(q+(\beta _{1}+\beta _{4})q^{2}-\beta _{9}q^{3}+(-\beta _{1}-\beta _{8}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(483, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(483, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)