Properties

Label 483.2.q
Level $483$
Weight $2$
Character orbit 483.q
Rep. character $\chi_{483}(64,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $240$
Newform subspaces $6$
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.q (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 6 \)
Sturm bound: \(128\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 680 240 440
Cusp forms 600 240 360
Eisenstein series 80 0 80

Trace form

\( 240 q + 4 q^{2} - 12 q^{4} + 8 q^{6} + 4 q^{7} + 12 q^{8} - 24 q^{9} + O(q^{10}) \) \( 240 q + 4 q^{2} - 12 q^{4} + 8 q^{6} + 4 q^{7} + 12 q^{8} - 24 q^{9} + 8 q^{10} + 16 q^{11} + 16 q^{13} + 4 q^{14} + 16 q^{15} - 32 q^{16} - 28 q^{17} + 4 q^{18} - 12 q^{19} + 40 q^{20} + 4 q^{21} - 24 q^{22} - 20 q^{23} + 24 q^{24} - 44 q^{25} - 32 q^{26} + 12 q^{28} - 12 q^{29} + 16 q^{30} + 12 q^{31} + 24 q^{32} + 8 q^{33} - 12 q^{34} + 8 q^{35} - 34 q^{36} - 4 q^{37} + 32 q^{38} - 72 q^{39} + 20 q^{40} - 64 q^{41} + 4 q^{42} + 4 q^{43} - 74 q^{44} - 112 q^{46} - 104 q^{47} - 144 q^{48} - 24 q^{49} - 70 q^{50} - 4 q^{51} + 96 q^{52} - 40 q^{53} - 36 q^{54} - 60 q^{55} + 36 q^{56} - 28 q^{57} + 58 q^{58} + 56 q^{59} + 12 q^{60} + 64 q^{61} + 120 q^{62} + 4 q^{63} - 44 q^{64} + 24 q^{65} + 64 q^{66} + 36 q^{67} + 112 q^{68} + 24 q^{69} + 8 q^{70} + 88 q^{71} + 12 q^{72} + 20 q^{73} + 122 q^{74} + 16 q^{75} - 148 q^{76} - 72 q^{77} + 8 q^{78} - 16 q^{79} + 224 q^{80} - 24 q^{81} - 104 q^{82} - 56 q^{83} + 12 q^{84} + 44 q^{85} - 232 q^{86} + 40 q^{87} + 162 q^{88} - 192 q^{89} + 8 q^{90} - 152 q^{91} + 168 q^{92} + 56 q^{93} + 136 q^{94} - 16 q^{95} + 8 q^{96} - 176 q^{97} - 18 q^{98} + 16 q^{99} + O(q^{100}) \)

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.q.a 483.q 23.c $10$ $3.857$ \(\Q(\zeta_{22})\) None \(4\) \(-1\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{11}]$ \(q+(-\zeta_{22}^{2}+\zeta_{22}^{3}+\zeta_{22}^{5}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
483.2.q.b 483.q 23.c $10$ $3.857$ \(\Q(\zeta_{22})\) None \(5\) \(-1\) \(-5\) \(-1\) $\mathrm{SU}(2)[C_{11}]$ \(q+(\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\zeta_{22}^{7}+\cdots)q^{2}+\cdots\)
483.2.q.c 483.q 23.c $20$ $3.857$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-4\) \(-2\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{11}]$ \(q+(-\beta _{2}-\beta _{6})q^{2}+\beta _{12}q^{3}+(-\beta _{5}+\cdots)q^{4}+\cdots\)
483.2.q.d 483.q 23.c $60$ $3.857$ None \(-1\) \(6\) \(-13\) \(-6\) $\mathrm{SU}(2)[C_{11}]$
483.2.q.e 483.q 23.c $60$ $3.857$ None \(-1\) \(6\) \(5\) \(6\) $\mathrm{SU}(2)[C_{11}]$
483.2.q.f 483.q 23.c $80$ $3.857$ None \(1\) \(-8\) \(13\) \(8\) $\mathrm{SU}(2)[C_{11}]$

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

\( S_{2}^{\mathrm{old}}(483, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)