Properties

Label 82.2.c
Level $82$
Weight $2$
Character orbit 82.c
Rep. character $\chi_{82}(9,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $3$
Sturm bound $21$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 82 = 2 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 82.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(21\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(82, [\chi])\).

Total New Old
Modular forms 26 6 20
Cusp forms 18 6 12
Eisenstein series 8 0 8

Trace form

\( 6q + 2q^{3} - 6q^{4} - 6q^{6} + O(q^{10}) \) \( 6q + 2q^{3} - 6q^{4} - 6q^{6} - 4q^{10} - 10q^{11} - 2q^{12} + 16q^{13} + 4q^{15} + 6q^{16} + 10q^{17} - 6q^{18} - 10q^{19} + 14q^{22} - 8q^{23} + 6q^{24} + 6q^{25} - 16q^{27} - 4q^{29} + 12q^{30} - 16q^{31} - 2q^{34} - 24q^{35} + 12q^{37} + 2q^{38} + 4q^{40} - 24q^{41} + 24q^{42} + 10q^{44} + 28q^{45} + 16q^{47} + 2q^{48} - 36q^{51} - 16q^{52} - 8q^{53} + 12q^{55} + 12q^{57} - 4q^{58} - 28q^{59} - 4q^{60} + 48q^{63} - 6q^{64} + 32q^{65} + 12q^{66} - 14q^{67} - 10q^{68} - 16q^{69} - 24q^{70} + 20q^{71} + 6q^{72} + 2q^{75} + 10q^{76} - 48q^{78} + 16q^{79} - 10q^{81} - 10q^{82} + 24q^{83} + 20q^{85} + 8q^{86} - 14q^{88} - 10q^{89} + 8q^{92} + 8q^{93} - 16q^{94} + 4q^{95} - 6q^{96} + 6q^{97} - 58q^{98} - 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(82, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
82.2.c.a \(2\) \(0.655\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}+(-1+i)q^{3}-q^{4}+2iq^{5}+\cdots\)
82.2.c.b \(2\) \(0.655\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(6\) \(q-iq^{2}-q^{4}-2iq^{5}+(3-3i)q^{7}+\cdots\)
82.2.c.c \(2\) \(0.655\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(-6\) \(q-iq^{2}+(2-2i)q^{3}-q^{4}+2iq^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(82, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(82, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 2}\)