Properties

Label 84.4.k
Level $84$
Weight $4$
Character orbit 84.k
Rep. character $\chi_{84}(5,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $3$
Sturm bound $64$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 84.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(64\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(84, [\chi])\).

Total New Old
Modular forms 108 16 92
Cusp forms 84 16 68
Eisenstein series 24 0 24

Trace form

\( 16q - 22q^{7} - 30q^{9} + O(q^{10}) \) \( 16q - 22q^{7} - 30q^{9} + 132q^{15} + 36q^{19} - 54q^{21} - 194q^{25} + 534q^{31} - 108q^{33} + 130q^{37} - 108q^{39} - 1040q^{43} - 342q^{45} - 932q^{49} - 300q^{51} + 1800q^{57} + 2148q^{61} + 1056q^{63} + 1100q^{67} + 486q^{73} - 3384q^{75} + 446q^{79} - 450q^{81} - 6144q^{85} - 2898q^{87} + 708q^{91} + 72q^{93} + 9216q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(84, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
84.4.k.a \(2\) \(4.956\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-9\) \(0\) \(-17\) \(q+(-3-3\zeta_{6})q^{3}+(-18+19\zeta_{6})q^{7}+\cdots\)
84.4.k.b \(2\) \(4.956\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(9\) \(0\) \(37\) \(q+(3+3\zeta_{6})q^{3}+(18+\zeta_{6})q^{7}+3^{3}\zeta_{6}q^{9}+\cdots\)
84.4.k.c \(12\) \(4.956\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-42\) \(q-\beta _{5}q^{3}-\beta _{9}q^{5}+(-1+2\beta _{1}-2\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(84, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(84, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)