Properties

Label 182.2.w
Level $182$
Weight $2$
Character orbit 182.w
Rep. character $\chi_{182}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $40$
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.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
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 128 40 88
Cusp forms 96 40 56
Eisenstein series 32 0 32

Trace form

\( 40q - 8q^{7} - 48q^{9} + O(q^{10}) \) \( 40q - 8q^{7} - 48q^{9} - 12q^{11} - 4q^{12} - 4q^{14} - 16q^{15} + 20q^{16} - 8q^{18} + 16q^{19} + 24q^{21} + 4q^{22} + 8q^{28} + 4q^{29} + 16q^{31} - 24q^{33} - 20q^{35} - 24q^{36} + 40q^{37} + 12q^{39} + 24q^{41} + 24q^{42} - 72q^{43} + 12q^{46} + 36q^{47} - 28q^{49} + 24q^{51} - 16q^{52} - 4q^{53} + 12q^{55} - 12q^{56} - 12q^{57} - 32q^{58} + 16q^{60} + 36q^{62} + 16q^{63} - 52q^{65} - 16q^{67} - 12q^{68} - 84q^{69} - 88q^{70} + 28q^{71} - 16q^{72} - 76q^{73} - 20q^{74} + 28q^{75} - 32q^{76} + 8q^{78} - 16q^{79} - 8q^{81} + 96q^{82} + 108q^{83} + 32q^{84} + 56q^{85} - 32q^{86} + 24q^{87} + 48q^{89} + 44q^{91} + 32q^{92} + 48q^{93} + 24q^{95} - 88q^{97} - 8q^{98} + 28q^{99} + O(q^{100}) \)

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.w.a \(40\) \(1.453\) None \(0\) \(0\) \(0\) \(-8\)

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

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