Properties

Label 144.2.i
Level $144$
Weight $2$
Character orbit 144.i
Rep. character $\chi_{144}(49,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $10$
Newform subspaces $4$
Sturm bound $48$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(144, [\chi])\).

Total New Old
Modular forms 60 14 46
Cusp forms 36 10 26
Eisenstein series 24 4 20

Trace form

\( 10q + 2q^{3} - q^{5} + q^{7} - 4q^{9} + O(q^{10}) \) \( 10q + 2q^{3} - q^{5} + q^{7} - 4q^{9} + 7q^{11} - q^{13} + 5q^{15} - 8q^{17} + 4q^{19} - 3q^{21} - 5q^{23} - 2q^{25} - 16q^{27} + 3q^{29} + 7q^{31} - 5q^{33} - 30q^{35} - 4q^{37} - 31q^{39} - 3q^{41} + 7q^{43} + 11q^{45} - 15q^{47} + 10q^{51} - 4q^{53} - 6q^{55} - 10q^{57} + 25q^{59} - q^{61} + 33q^{63} + 17q^{65} + q^{67} + 13q^{69} + 56q^{71} - 16q^{73} + 46q^{75} + 21q^{77} + q^{79} + 20q^{81} + 29q^{83} - 6q^{85} + 15q^{87} + 12q^{89} - 22q^{91} + 5q^{93} - 28q^{95} + 5q^{97} - 47q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
144.2.i.a \(2\) \(1.150\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-1\) \(q+(1-2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
144.2.i.b \(2\) \(1.150\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-3\) \(q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots\)
144.2.i.c \(2\) \(1.150\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(2\) \(q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
144.2.i.d \(4\) \(1.150\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-1\) \(1\) \(3\) \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)