Properties

Label 546.2.e
Level $546$
Weight $2$
Character orbit 546.e
Rep. character $\chi_{546}(545,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $8$
Sturm bound $224$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(224\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(5\), \(17\), \(19\), \(71\)

Dimensions

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

Total New Old
Modular forms 120 40 80
Cusp forms 104 40 64
Eisenstein series 16 0 16

Trace form

\( 40q + 40q^{4} - 8q^{9} + O(q^{10}) \) \( 40q + 40q^{4} - 8q^{9} + 40q^{16} - 56q^{25} + 4q^{30} - 8q^{36} + 12q^{39} + 14q^{42} - 48q^{43} + 28q^{49} - 12q^{51} + 40q^{64} - 4q^{78} - 120q^{79} + 16q^{81} - 36q^{91} + O(q^{100}) \)

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.e.a \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(0\) \(-5\) \(q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+2\zeta_{6})q^{5}+\cdots\)
546.2.e.b \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(-2\) \(3\) \(0\) \(5\) \(q-q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(1-2\zeta_{6})q^{5}+\cdots\)
546.2.e.c \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(0\) \(5\) \(q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(1-2\zeta_{6})q^{5}+\cdots\)
546.2.e.d \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(0\) \(-5\) \(q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1+2\zeta_{6})q^{5}+\cdots\)
546.2.e.e \(8\) \(4.360\) 8.0.303595776.1 None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{5}+\beta _{7})q^{5}+\cdots\)
546.2.e.f \(8\) \(4.360\) 8.0.\(\cdots\).11 None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{7}q^{3}+q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots\)
546.2.e.g \(8\) \(4.360\) 8.0.303595776.1 None \(8\) \(0\) \(0\) \(0\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{5}-\beta _{7})q^{5}+\cdots\)
546.2.e.h \(8\) \(4.360\) 8.0.\(\cdots\).11 None \(8\) \(0\) \(0\) \(0\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots\)

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

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