Properties

Label 14.6.c
Level $14$
Weight $6$
Character orbit 14.c
Rep. character $\chi_{14}(9,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $2$
Sturm bound $12$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 14.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(14, [\chi])\).

Total New Old
Modular forms 24 8 16
Cusp forms 16 8 8
Eisenstein series 8 0 8

Trace form

\( 8 q - 64 q^{4} - 28 q^{5} + 224 q^{6} + 232 q^{7} - 896 q^{9} - 448 q^{10} + 232 q^{11} + 3360 q^{13} + 272 q^{14} - 3488 q^{15} - 1024 q^{16} - 2996 q^{17} + 1632 q^{18} + 616 q^{19} + 896 q^{20} + 8692 q^{21}+ \cdots + 558832 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
14.6.c.a 14.c 7.c $4$ $2.245$ \(\Q(\sqrt{-3}, \sqrt{79})\) None 14.6.c.a \(-8\) \(-14\) \(-70\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\beta _{2}q^{2}+(-7-\beta _{1}-7\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
14.6.c.b 14.c 7.c $4$ $2.245$ \(\Q(\sqrt{-3}, \sqrt{130})\) None 14.6.c.b \(8\) \(14\) \(42\) \(232\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\beta _{2}q^{2}+(7-\beta _{1}+7\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(14, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)