Properties

Label 182.2.n
Level $182$
Weight $2$
Character orbit 182.n
Rep. character $\chi_{182}(25,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $2$
Sturm bound $56$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 182.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(56\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 64 16 48
Cusp forms 48 16 32
Eisenstein series 16 0 16

Trace form

\( 16q + 8q^{4} + 4q^{9} + O(q^{10}) \) \( 16q + 8q^{4} + 4q^{9} - 4q^{10} + 4q^{13} + 2q^{14} - 8q^{16} - 10q^{17} - 4q^{22} + 12q^{23} + 4q^{25} - 6q^{26} - 12q^{27} + 20q^{29} - 14q^{30} - 36q^{35} + 8q^{36} - 14q^{38} - 24q^{39} + 4q^{40} + 8q^{42} - 22q^{49} - 22q^{51} + 2q^{52} + 2q^{53} - 40q^{55} + 10q^{56} - 26q^{61} + 12q^{62} - 16q^{64} + 24q^{65} - 16q^{66} + 10q^{68} + 8q^{69} - 24q^{74} + 56q^{75} + 48q^{77} + 32q^{78} - 16q^{79} + 24q^{81} + 8q^{82} + 32q^{87} - 2q^{88} + 52q^{90} - 8q^{91} + 24q^{92} + 22q^{94} + O(q^{100}) \)

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.n.a \(4\) \(1.453\) \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) \(q+\zeta_{12}q^{2}-2\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
182.2.n.b \(12\) \(1.453\) 12.0.\(\cdots\).1 None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{10}q^{2}+(1-\beta _{7}+\beta _{9})q^{3}+(1-\beta _{7}+\cdots)q^{4}+\cdots\)

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

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