Properties

Label 546.2.o
Level $546$
Weight $2$
Character orbit 546.o
Rep. character $\chi_{546}(265,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $4$
Sturm bound $224$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(224\)
Trace bound: \(11\)
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 32 208
Cusp forms 208 32 176
Eisenstein series 32 0 32

Trace form

\( 32q - 4q^{7} - 32q^{9} + O(q^{10}) \) \( 32q - 4q^{7} - 32q^{9} - 16q^{11} - 8q^{14} - 32q^{16} - 12q^{21} - 16q^{22} - 4q^{28} + 16q^{35} - 24q^{37} + 40q^{39} - 16q^{44} + 8q^{46} + 32q^{50} + 32q^{53} - 24q^{57} - 24q^{58} + 4q^{63} - 64q^{65} + 80q^{67} + 56q^{70} + 80q^{71} + 32q^{74} - 8q^{78} - 48q^{79} + 32q^{81} - 12q^{84} + 80q^{85} - 80q^{86} - 36q^{91} - 16q^{92} - 56q^{93} - 48q^{98} + 16q^{99} + O(q^{100}) \)

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.o.a \(8\) \(4.360\) 8.0.7442857984.4 None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{2}q^{2}-\beta _{6}q^{3}+\beta _{6}q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots\)
546.2.o.b \(8\) \(4.360\) 8.0.836829184.2 None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{2}q^{2}+\beta _{7}q^{3}+\beta _{7}q^{4}+(\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
546.2.o.c \(8\) \(4.360\) 8.0.836829184.2 None \(0\) \(0\) \(4\) \(-8\) \(q+\beta _{3}q^{2}+\beta _{7}q^{3}-\beta _{7}q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
546.2.o.d \(8\) \(4.360\) 8.0.7442857984.4 None \(0\) \(0\) \(4\) \(4\) \(q-\beta _{2}q^{2}+\beta _{6}q^{3}+\beta _{6}q^{4}+(-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)