Properties

Label 21.4.e
Level $21$
Weight $4$
Character orbit 21.e
Rep. character $\chi_{21}(4,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $2$
Sturm bound $10$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 21.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(21, [\chi])\).

Total New Old
Modular forms 20 8 12
Cusp forms 12 8 4
Eisenstein series 8 0 8

Trace form

\( 8 q + 2 q^{2} + 6 q^{3} - 26 q^{4} - 8 q^{5} - 24 q^{6} - 20 q^{7} + 120 q^{8} - 36 q^{9} + 46 q^{10} - 20 q^{11} + 72 q^{12} - 4 q^{13} - 242 q^{14} - 84 q^{15} - 170 q^{16} - 132 q^{17} + 18 q^{18} + 218 q^{19}+ \cdots + 360 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
21.4.e.a 21.e 7.c $2$ $1.239$ \(\Q(\sqrt{-3}) \) None 21.4.e.a \(3\) \(-3\) \(3\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{2}-3\zeta_{6}q^{3}-\zeta_{6}q^{4}+(3+\cdots)q^{5}+\cdots\)
21.4.e.b 21.e 7.c $6$ $1.239$ 6.0.9924270768.1 None 21.4.e.b \(-1\) \(9\) \(-11\) \(-13\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(3-3\beta _{4})q^{3}+(-8+\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(21, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(21, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)