Properties

Label 546.2.p
Level $546$
Weight $2$
Character orbit 546.p
Rep. character $\chi_{546}(239,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $4$
Sturm bound $224$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(224\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(546, [\chi])\).

Total New Old
Modular forms 240 56 184
Cusp forms 208 56 152
Eisenstein series 32 0 32

Trace form

\( 56q + O(q^{10}) \) \( 56q - 56q^{16} + 8q^{18} - 16q^{19} - 8q^{21} + 48q^{27} + 16q^{31} - 48q^{33} + 16q^{37} - 16q^{39} - 32q^{45} - 8q^{46} + 48q^{54} + 32q^{55} + 80q^{57} - 8q^{58} + 32q^{61} - 8q^{63} + 32q^{66} - 24q^{67} + 8q^{72} - 16q^{73} - 16q^{76} + 80q^{78} - 80q^{79} - 48q^{81} + 8q^{84} + 80q^{85} - 8q^{91} - 48q^{93} + 16q^{94} + 128q^{97} - 88q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(546, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
546.2.p.a \(8\) \(4.360\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{4}q^{2}+(\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
546.2.p.b \(8\) \(4.360\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(4\) \(0\) \(q-\beta _{4}q^{2}+(-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
546.2.p.c \(20\) \(4.360\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{8}q^{2}+\beta _{11}q^{3}-\beta _{4}q^{4}+(\beta _{4}+2\beta _{5}+\cdots)q^{5}+\cdots\)
546.2.p.d \(20\) \(4.360\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(4\) \(0\) \(q-\beta _{8}q^{2}-\beta _{19}q^{3}-\beta _{4}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(546, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)