Properties

Label 156.2.u
Level $156$
Weight $2$
Character orbit 156.u
Rep. character $\chi_{156}(41,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $20$
Newform subspaces $2$
Sturm bound $56$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 156.u (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(56\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(156, [\chi])\).

Total New Old
Modular forms 136 20 116
Cusp forms 88 20 68
Eisenstein series 48 0 48

Trace form

\( 20q - 2q^{7} + O(q^{10}) \) \( 20q - 2q^{7} + 12q^{15} + 10q^{19} - 12q^{21} - 36q^{27} - 10q^{31} - 30q^{33} + 2q^{37} - 42q^{43} - 30q^{45} - 18q^{49} + 18q^{57} + 30q^{63} - 32q^{67} + 78q^{69} + 10q^{73} + 90q^{75} + 96q^{79} - 12q^{81} + 96q^{85} + 22q^{91} + 48q^{93} + 38q^{97} - 18q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(156, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
156.2.u.a \(4\) \(1.246\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(2\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}-3\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
156.2.u.b \(16\) \(1.246\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) \(q+(-\beta _{9}-\beta _{13}-\beta _{15})q^{3}+(-\beta _{3}-\beta _{9}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(156, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(156, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)