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

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

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

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