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Properties

Label 546.4.l
Level $546$
Weight $4$
Character orbit 546.l
Rep. character $\chi_{546}(211,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $10$
Sturm bound $448$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 546.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
Sturm bound: \(448\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(546, [\chi])\).

Total New Old
Modular forms 688 80 608
Cusp forms 656 80 576
Eisenstein series 32 0 32

Trace form

\( 80 q - 8 q^{2} - 160 q^{4} - 40 q^{5} + 64 q^{8} - 360 q^{9} + 40 q^{10} - 80 q^{11} - 212 q^{13} - 48 q^{15} - 640 q^{16} + 132 q^{17} + 144 q^{18} - 96 q^{19} + 80 q^{20} + 176 q^{22} + 232 q^{23} + 760 q^{25}+ \cdots + 1440 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(546, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
546.4.l.a 546.l 13.c $2$ $32.215$ \(\Q(\sqrt{-3}) \) None 546.4.l.a \(-2\) \(-3\) \(14\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}+\cdots\)
546.4.l.b 546.l 13.c $2$ $32.215$ \(\Q(\sqrt{-3}) \) None 546.4.l.b \(-2\) \(3\) \(44\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
546.4.l.c 546.l 13.c $8$ $32.215$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 546.4.l.c \(8\) \(-12\) \(20\) \(28\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{1}q^{2}+3\beta _{1}q^{3}+(-4-4\beta _{1})q^{4}+\cdots\)
546.4.l.d 546.l 13.c $8$ $32.215$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 546.4.l.d \(8\) \(12\) \(0\) \(-28\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{1}q^{2}-3\beta _{1}q^{3}+(-4-4\beta _{1})q^{4}+\cdots\)
546.4.l.e 546.l 13.c $10$ $32.215$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 546.4.l.e \(-10\) \(-15\) \(-24\) \(35\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{3}q^{2}-3\beta _{3}q^{3}+(-4+4\beta _{3})q^{4}+\cdots\)
546.4.l.f 546.l 13.c $10$ $32.215$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 546.4.l.f \(-10\) \(-15\) \(-22\) \(-35\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{1}q^{2}+3\beta _{1}q^{3}+(-4-4\beta _{1})q^{4}+\cdots\)
546.4.l.g 546.l 13.c $10$ $32.215$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 546.4.l.g \(-10\) \(15\) \(-34\) \(-35\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2-2\beta _{3})q^{2}+(3+3\beta _{3})q^{3}+4\beta _{3}q^{4}+\cdots\)
546.4.l.h 546.l 13.c $10$ $32.215$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 546.4.l.h \(-10\) \(15\) \(-18\) \(35\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{3}q^{2}+3\beta _{3}q^{3}+(-4+4\beta _{3})q^{4}+\cdots\)
546.4.l.i 546.l 13.c $10$ $32.215$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 546.4.l.i \(10\) \(-15\) \(8\) \(-35\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{3})q^{2}+(-3-3\beta _{3})q^{3}+4\beta _{3}q^{4}+\cdots\)
546.4.l.j 546.l 13.c $10$ $32.215$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 546.4.l.j \(10\) \(15\) \(-28\) \(35\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{6})q^{2}+(3-3\beta _{6})q^{3}-4\beta _{6}q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(546, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(546, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)