Properties

Label 84.2.o
Level $84$
Weight $2$
Character orbit 84.o
Rep. character $\chi_{84}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $2$
Sturm bound $32$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 84.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(84, [\chi])\).

Total New Old
Modular forms 40 16 24
Cusp forms 24 16 8
Eisenstein series 16 0 16

Trace form

\( 16 q + 2 q^{2} - 2 q^{4} + 8 q^{8} - 8 q^{9} + O(q^{10}) \) \( 16 q + 2 q^{2} - 2 q^{4} + 8 q^{8} - 8 q^{9} - 18 q^{10} - 22 q^{14} - 10 q^{16} + 2 q^{18} - 8 q^{21} - 12 q^{22} + 18 q^{24} + 4 q^{25} + 30 q^{26} + 6 q^{28} - 32 q^{29} + 8 q^{30} + 12 q^{32} - 12 q^{33} + 4 q^{36} + 12 q^{37} + 18 q^{38} - 30 q^{40} + 16 q^{42} - 4 q^{44} + 12 q^{46} + 8 q^{49} + 4 q^{50} + 36 q^{52} - 8 q^{53} + 40 q^{56} + 24 q^{57} + 14 q^{58} - 22 q^{60} + 24 q^{61} + 4 q^{64} + 8 q^{65} - 36 q^{66} - 36 q^{68} + 38 q^{70} - 4 q^{72} - 36 q^{73} - 38 q^{74} + 16 q^{77} - 12 q^{78} - 72 q^{80} - 8 q^{81} - 24 q^{82} - 40 q^{84} - 64 q^{85} - 6 q^{86} - 26 q^{88} - 56 q^{92} + 12 q^{93} + 30 q^{96} - 72 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(84, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
84.2.o.a $8$ $0.671$ 8.0.562828176.1 None \(1\) \(-4\) \(0\) \(2\) \(q-\beta _{4}q^{2}+(-1+\beta _{3})q^{3}+(\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
84.2.o.b $8$ $0.671$ 8.0.562828176.1 None \(1\) \(4\) \(0\) \(-2\) \(q+\beta _{6}q^{2}+\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(84, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(84, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)