Properties

Label 14.4.c
Level $14$
Weight $4$
Character orbit 14.c
Rep. character $\chi_{14}(9,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $4$
Newform subspaces $2$
Sturm bound $8$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(8\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(14, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4 q + 6 q^{3} - 8 q^{4} + 2 q^{5} - 16 q^{6} - 48 q^{7} + 28 q^{9} + 32 q^{10} + 22 q^{11} + 24 q^{12} - 8 q^{13} + 104 q^{14} + 76 q^{15} - 32 q^{16} - 110 q^{17} - 48 q^{18} - 142 q^{19} - 16 q^{20} - 2 q^{21}+ \cdots - 1592 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
14.4.c.a 14.c 7.c $2$ $0.826$ \(\Q(\sqrt{-3}) \) None 14.4.c.a \(-2\) \(5\) \(9\) \(-28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}+5\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots\)
14.4.c.b 14.c 7.c $2$ $0.826$ \(\Q(\sqrt{-3}) \) None 14.4.c.b \(2\) \(1\) \(-7\) \(-20\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-7+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(14, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)