Properties

Label 182.2.ba
Level $182$
Weight $2$
Character orbit 182.ba
Rep. character $\chi_{182}(41,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $32$
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.ba (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 32 96
Cusp forms 96 32 64
Eisenstein series 32 0 32

Trace form

\( 32q - 4q^{7} + 8q^{9} + O(q^{10}) \) \( 32q - 4q^{7} + 8q^{9} + 8q^{14} - 16q^{15} + 16q^{16} - 8q^{18} - 24q^{21} - 8q^{22} - 4q^{28} - 8q^{29} - 24q^{30} + 28q^{35} - 24q^{36} - 48q^{37} + 32q^{39} + 24q^{42} - 24q^{43} - 24q^{44} + 24q^{49} - 64q^{53} - 12q^{56} - 8q^{57} + 40q^{58} - 8q^{60} - 60q^{63} - 40q^{65} + 64q^{67} + 8q^{70} - 32q^{71} + 32q^{72} - 8q^{74} + 8q^{78} + 128q^{79} - 40q^{81} + 24q^{84} + 32q^{85} - 8q^{86} + 8q^{91} + 32q^{92} - 56q^{93} + 120q^{95} - 32q^{98} + 88q^{99} + O(q^{100}) \)

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.ba.a \(32\) \(1.453\) None \(0\) \(0\) \(0\) \(-4\)

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

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