Properties

Label 546.2.g
Level $546$
Weight $2$
Character orbit 546.g
Rep. character $\chi_{546}(209,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $4$
Sturm bound $224$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(224\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 120 32 88
Cusp forms 104 32 72
Eisenstein series 16 0 16

Trace form

\( 32q - 32q^{4} - 4q^{7} + 8q^{9} + O(q^{10}) \) \( 32q - 32q^{4} - 4q^{7} + 8q^{9} + 24q^{15} + 32q^{16} - 16q^{21} + 48q^{25} + 4q^{28} + 4q^{30} - 8q^{36} - 24q^{37} + 22q^{42} - 64q^{43} + 40q^{46} + 52q^{49} - 52q^{51} - 32q^{57} - 40q^{58} - 24q^{60} - 20q^{63} - 32q^{64} - 48q^{70} + 72q^{79} + 40q^{81} + 16q^{84} + 64q^{85} - 8q^{91} + 56q^{93} + O(q^{100}) \)

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.g.a \(4\) \(4.360\) \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(4\) \(6\) \(q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
546.2.g.b \(4\) \(4.360\) \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(-4\) \(6\) \(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
546.2.g.c \(12\) \(4.360\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-2\) \(4\) \(-8\) \(q-\beta _{5}q^{2}+\beta _{3}q^{3}-q^{4}-\beta _{4}q^{5}+\beta _{6}q^{6}+\cdots\)
546.2.g.d \(12\) \(4.360\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(2\) \(-4\) \(-8\) \(q-\beta _{5}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{4}q^{5}-\beta _{6}q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)