Properties

Label 182.2.i
Level $182$
Weight $2$
Character orbit 182.i
Rep. character $\chi_{182}(83,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $1$
Sturm bound $56$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 182.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(56\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(182, [\chi])\).

Total New Old
Modular forms 64 24 40
Cusp forms 48 24 24
Eisenstein series 16 0 16

Trace form

\( 24q + 8q^{7} - 40q^{9} + O(q^{10}) \) \( 24q + 8q^{7} - 40q^{9} + 4q^{14} + 16q^{15} - 24q^{16} + 8q^{18} + 4q^{21} + 8q^{22} + 8q^{28} - 16q^{29} + 20q^{35} - 8q^{37} - 40q^{39} + 12q^{42} - 24q^{50} + 16q^{53} + 16q^{57} + 8q^{58} - 16q^{60} - 40q^{63} + 88q^{65} - 96q^{67} - 44q^{70} - 64q^{71} - 8q^{72} - 16q^{74} + 16q^{78} - 8q^{79} + 168q^{81} + 4q^{84} - 56q^{85} + 56q^{86} + 44q^{91} - 8q^{92} + 112q^{93} + 32q^{98} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(182, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
182.2.i.a \(24\) \(1.453\) None \(0\) \(0\) \(0\) \(8\)

Decomposition of \(S_{2}^{\mathrm{old}}(182, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(182, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)