Properties

Label 182.2.bc
Level $182$
Weight $2$
Character orbit 182.bc
Rep. character $\chi_{182}(45,\cdot)$
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.bc (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

\( 40q - 4q^{7} + 24q^{9} + O(q^{10}) \) \( 40q - 4q^{7} + 24q^{9} + 4q^{12} - 4q^{14} - 16q^{15} - 40q^{16} - 8q^{18} - 16q^{19} - 4q^{21} + 4q^{22} - 8q^{28} + 4q^{29} + 24q^{30} - 4q^{31} + 36q^{33} + 28q^{35} - 24q^{36} - 8q^{37} - 24q^{39} - 24q^{41} - 12q^{42} - 72q^{43} + 12q^{44} + 4q^{49} - 24q^{51} + 4q^{52} - 4q^{53} + 36q^{54} - 12q^{55} - 12q^{56} - 12q^{57} - 8q^{58} - 8q^{60} - 12q^{61} - 36q^{62} - 108q^{63} - 16q^{65} + 44q^{67} + 84q^{69} + 8q^{70} + 28q^{71} + 8q^{72} - 44q^{73} + 40q^{74} + 56q^{75} + 32q^{76} + 8q^{78} - 16q^{79} + 4q^{81} + 48q^{82} - 108q^{83} + 24q^{84} + 56q^{85} + 52q^{86} - 12q^{89} + 52q^{91} + 32q^{92} - 24q^{93} + 48q^{94} + 88q^{97} + 88q^{98} + 28q^{99} + O(q^{100}) \)

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.bc.a \(40\) \(1.453\) None \(0\) \(0\) \(0\) \(-4\)

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

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