Properties

Label 483.2.d
Level $483$
Weight $2$
Character orbit 483.d
Rep. character $\chi_{483}(461,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $4$
Sturm bound $128$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(128\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

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

Total New Old
Modular forms 68 60 8
Cusp forms 60 60 0
Eisenstein series 8 0 8

Trace form

\( 60q - 64q^{4} - 4q^{7} + 4q^{9} + O(q^{10}) \) \( 60q - 64q^{4} - 4q^{7} + 4q^{9} - 8q^{15} + 72q^{16} - 20q^{18} + 6q^{21} + 16q^{22} + 44q^{25} + 4q^{28} - 4q^{30} + 4q^{36} - 32q^{37} - 8q^{39} - 16q^{42} - 48q^{43} + 36q^{49} - 36q^{51} + 44q^{57} + 32q^{58} - 44q^{60} - 22q^{63} - 88q^{64} + 48q^{67} - 40q^{70} + 64q^{72} - 60q^{78} - 24q^{79} + 4q^{81} + 10q^{84} - 40q^{85} - 20q^{91} - 36q^{99} + O(q^{100}) \)

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.d.a \(4\) \(3.857\) \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(-6\) \(6\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
483.2.d.b \(4\) \(3.857\) \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(6\) \(6\) \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
483.2.d.c \(8\) \(3.857\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(-8\) \(q-\zeta_{16}^{4}q^{2}+(\zeta_{16}+\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}+\cdots\)
483.2.d.d \(44\) \(3.857\) None \(0\) \(0\) \(0\) \(-8\)