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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
483.2.i.a 483.i 7.c $2$ $3.857$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
483.2.i.b 483.i 7.c $2$ $3.857$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
483.2.i.c 483.i 7.c $2$ $3.857$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
483.2.i.d 483.i 7.c $2$ $3.857$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
483.2.i.e 483.i 7.c $4$ $3.857$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(1\) \(-2\) \(1\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
483.2.i.f 483.i 7.c $12$ $3.857$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(6\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{5})q^{2}+\beta _{7}q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots\)
483.2.i.g 483.i 7.c $16$ $3.857$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-1\) \(-8\) \(-5\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{5})q^{2}+(-1-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
483.2.i.h 483.i 7.c $20$ $3.857$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-3\) \(10\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{4})q^{2}-\beta _{9}q^{3}+(-\beta _{1}-\beta _{8}+\cdots)q^{4}+\cdots\)

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

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