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

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

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

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

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