Properties

Label 546.2.i
Level $546$
Weight $2$
Character orbit 546.i
Rep. character $\chi_{546}(79,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $11$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 11 \)
Sturm bound: \(224\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(17\)

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

\( 32 q - 16 q^{4} + 8 q^{5} + 8 q^{6} - 12 q^{7} - 16 q^{9} + 4 q^{10} + 8 q^{11} + 8 q^{13} - 4 q^{14} - 8 q^{15} - 16 q^{16} - 12 q^{17} - 8 q^{19} - 16 q^{20} - 4 q^{24} - 20 q^{25} + 12 q^{28} - 24 q^{29}+ \cdots - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
546.2.i.a 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None 546.2.i.a \(-1\) \(-1\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.b 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None 546.2.i.b \(-1\) \(-1\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.c 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None 546.2.i.c \(-1\) \(-1\) \(4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.d 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None 546.2.i.d \(-1\) \(1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.e 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None 546.2.i.e \(1\) \(-1\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.f 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None 546.2.i.f \(1\) \(1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.g 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None 546.2.i.g \(1\) \(1\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.h 546.i 7.c $4$ $4.360$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 546.2.i.h \(-2\) \(-2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
546.2.i.i 546.i 7.c $4$ $4.360$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 546.2.i.i \(-2\) \(2\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
546.2.i.j 546.i 7.c $4$ $4.360$ \(\Q(\sqrt{-3}, \sqrt{7})\) None 546.2.i.j \(2\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
546.2.i.k 546.i 7.c $6$ $4.360$ 6.0.21870000.1 None 546.2.i.k \(3\) \(3\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)