Properties

Label 182.2.e
Level $182$
Weight $2$
Character orbit 182.e
Rep. character $\chi_{182}(107,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $4$
Sturm bound $56$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 182.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(56\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 64 20 44
Cusp forms 48 20 28
Eisenstein series 16 0 16

Trace form

\( 20q - 2q^{3} + 20q^{4} - 6q^{7} - 8q^{9} + O(q^{10}) \) \( 20q - 2q^{3} + 20q^{4} - 6q^{7} - 8q^{9} - 4q^{10} - 10q^{11} - 2q^{12} - 6q^{13} - 4q^{15} + 20q^{16} + 12q^{17} - 6q^{21} + 2q^{22} - 18q^{25} - 6q^{26} + 4q^{27} - 6q^{28} + 2q^{29} + 10q^{30} - 22q^{31} + 16q^{33} + 12q^{35} - 8q^{36} - 40q^{37} - 10q^{38} + 34q^{39} - 4q^{40} - 2q^{41} - 26q^{42} + 8q^{43} - 10q^{44} - 40q^{45} - 16q^{46} + 6q^{47} - 2q^{48} - 22q^{49} + 12q^{50} + 14q^{51} - 6q^{52} - 8q^{53} + 12q^{54} + 2q^{55} - 28q^{57} + 16q^{59} - 4q^{60} - 24q^{61} - 20q^{62} + 66q^{63} + 20q^{64} - 2q^{65} - 16q^{66} + 12q^{68} - 26q^{69} + 40q^{70} - 26q^{71} + 28q^{73} - 60q^{75} - 10q^{77} - 12q^{78} - 10q^{79} + 22q^{81} - 16q^{82} + 84q^{83} - 6q^{84} + 20q^{85} + 10q^{86} + 80q^{87} + 2q^{88} + 28q^{89} + 28q^{90} + 6q^{91} - 8q^{93} - 32q^{94} - 8q^{95} + 34q^{97} + 48q^{98} + 52q^{99} + O(q^{100}) \)

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.e.a \(2\) \(1.453\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-1\) \(-1\) \(4\) \(q-q^{2}-\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)
182.2.e.b \(2\) \(1.453\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-1\) \(3\) \(-4\) \(q-q^{2}-\zeta_{6}q^{3}+q^{4}+3\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)
182.2.e.c \(6\) \(1.453\) 6.0.4740147.1 None \(-6\) \(1\) \(0\) \(-3\) \(q-q^{2}+\beta _{4}q^{3}+q^{4}+(\beta _{4}+\beta _{5})q^{5}+\cdots\)
182.2.e.d \(10\) \(1.453\) 10.0.\(\cdots\).1 None \(10\) \(-1\) \(-2\) \(-3\) \(q+q^{2}-\beta _{5}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{5}q^{6}+\cdots\)

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

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