Properties

Label 84.2.b
Level 84
Weight 2
Character orbit b
Rep. character \(\chi_{84}(55,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(19\)

Dimensions

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

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(84, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
84.2.b.a \(4\) \(0.671\) 4.0.2312.1 None \(-1\) \(-4\) \(0\) \(2\) \(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
84.2.b.b \(4\) \(0.671\) 4.0.2312.1 None \(-1\) \(4\) \(0\) \(-2\) \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)

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

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