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Properties

Label 342.4.g
Level $342$
Weight $4$
Character orbit 342.g
Rep. character $\chi_{342}(163,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $50$
Newform subspaces $10$
Sturm bound $240$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 342.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
Sturm bound: \(240\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(342, [\chi])\).

Total New Old
Modular forms 376 50 326
Cusp forms 344 50 294
Eisenstein series 32 0 32

Trace form

\( 50 q - 2 q^{2} - 100 q^{4} + 8 q^{5} + 60 q^{7} + 16 q^{8} + 20 q^{10} + 134 q^{11} - 72 q^{13} - 12 q^{14} - 400 q^{16} - 12 q^{17} + 243 q^{19} - 64 q^{20} + 126 q^{22} - 46 q^{23} - 861 q^{25} + 344 q^{26}+ \cdots - 2434 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(342, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
342.4.g.a 342.g 19.c $2$ $20.179$ \(\Q(\sqrt{-3}) \) None 114.4.e.b \(-2\) \(0\) \(-6\) \(38\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-6+6\zeta_{6})q^{5}+\cdots\)
342.4.g.b 342.g 19.c $2$ $20.179$ \(\Q(\sqrt{-3}) \) None 114.4.e.a \(-2\) \(0\) \(2\) \(-42\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(2-2\zeta_{6})q^{5}+\cdots\)
342.4.g.c 342.g 19.c $2$ $20.179$ \(\Q(\sqrt{-3}) \) None 38.4.c.b \(2\) \(0\) \(-12\) \(16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-12+12\zeta_{6})q^{5}+\cdots\)
342.4.g.d 342.g 19.c $2$ $20.179$ \(\Q(\sqrt{-3}) \) None 38.4.c.a \(2\) \(0\) \(3\) \(-64\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
342.4.g.e 342.g 19.c $4$ $20.179$ \(\Q(\sqrt{-3}, \sqrt{-10})\) None 114.4.e.c \(4\) \(0\) \(8\) \(36\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{1}q^{2}+(-4+4\beta _{1})q^{4}+(4\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
342.4.g.f 342.g 19.c $6$ $20.179$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 38.4.c.c \(-6\) \(0\) \(1\) \(52\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{4}q^{2}+(-4+4\beta _{4})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
342.4.g.g 342.g 19.c $6$ $20.179$ 6.0.6967728.1 None 114.4.e.e \(-6\) \(0\) \(2\) \(-34\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{3}q^{2}+(-4-4\beta _{3})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
342.4.g.h 342.g 19.c $6$ $20.179$ 6.0.627014547.1 None 114.4.e.d \(6\) \(0\) \(10\) \(14\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{1}q^{2}+(-4+4\beta _{1})q^{4}+(3\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
342.4.g.i 342.g 19.c $10$ $20.179$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 342.4.g.i \(-10\) \(0\) \(10\) \(22\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\beta _{1})q^{2}-4\beta _{1}q^{4}+(2-2\beta _{1}+\cdots)q^{5}+\cdots\)
342.4.g.j 342.g 19.c $10$ $20.179$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 342.4.g.i \(10\) \(0\) \(-10\) \(22\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{1})q^{2}-4\beta _{1}q^{4}+(-2+2\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(342, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)