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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
546.2.o.a 546.o 91.i $8$ $4.360$ 8.0.7442857984.4 None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{2}-\beta _{6}q^{3}+\beta _{6}q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots\)
546.2.o.b 546.o 91.i $8$ $4.360$ 8.0.836829184.2 None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+\beta _{7}q^{3}+\beta _{7}q^{4}+(\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
546.2.o.c 546.o 91.i $8$ $4.360$ 8.0.836829184.2 None \(0\) \(0\) \(4\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}+\beta _{7}q^{3}-\beta _{7}q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
546.2.o.d 546.o 91.i $8$ $4.360$ 8.0.7442857984.4 None \(0\) \(0\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{2}+\beta _{6}q^{3}+\beta _{6}q^{4}+(-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)

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

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