Properties

Label 483.2.h
Level $483$
Weight $2$
Character orbit 483.h
Rep. character $\chi_{483}(160,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $3$
Sturm bound $128$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(128\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 68 32 36
Cusp forms 60 32 28
Eisenstein series 8 0 8

Trace form

\( 32q - 4q^{2} + 36q^{4} - 12q^{8} - 32q^{9} + O(q^{10}) \) \( 32q - 4q^{2} + 36q^{4} - 12q^{8} - 32q^{9} + 44q^{16} + 4q^{18} - 8q^{23} + 24q^{25} - 68q^{32} + 16q^{35} - 36q^{36} - 40q^{46} + 16q^{49} + 12q^{50} - 48q^{58} + 84q^{64} + 16q^{70} + 40q^{71} + 12q^{72} - 72q^{77} + 8q^{78} + 32q^{81} - 136q^{85} + 16q^{92} - 24q^{93} - 16q^{95} - 28q^{98} + O(q^{100}) \)

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.h.a \(8\) \(3.857\) 8.0.342102016.5 None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{1}q^{3}-q^{4}+(\beta _{4}-\beta _{5})q^{5}+\cdots\)
483.2.h.b \(12\) \(3.857\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{8}q^{2}-\beta _{5}q^{3}+(1-\beta _{7})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
483.2.h.c \(12\) \(3.857\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(4\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{9}q^{3}+(3+\beta _{7})q^{4}-\beta _{5}q^{5}+\cdots\)

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

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