Properties

Label 144.3.q
Level $144$
Weight $3$
Character orbit 144.q
Rep. character $\chi_{144}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $22$
Newform subspaces $5$
Sturm bound $72$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(72\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(144, [\chi])\).

Total New Old
Modular forms 108 26 82
Cusp forms 84 22 62
Eisenstein series 24 4 20

Trace form

\( 22q + 2q^{3} - 3q^{5} + q^{7} + 2q^{9} + O(q^{10}) \) \( 22q + 2q^{3} - 3q^{5} + q^{7} + 2q^{9} + 3q^{11} - q^{13} + 35q^{15} + 4q^{19} + 15q^{21} + 3q^{23} + 34q^{25} + 74q^{27} - 75q^{29} - 23q^{31} - 23q^{33} - 4q^{37} - 55q^{39} - 39q^{41} + 49q^{43} + 53q^{45} - 213q^{47} - 36q^{49} - 152q^{51} + 54q^{55} - 40q^{57} - 213q^{59} - q^{61} - 135q^{63} - 147q^{65} + q^{67} + 13q^{69} - 28q^{73} + 82q^{75} + 141q^{77} + q^{79} + 122q^{81} + 363q^{83} + 24q^{85} + 387q^{87} + 98q^{91} - 97q^{93} + 726q^{95} - 61q^{97} + 499q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
144.3.q.a \(2\) \(3.924\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(6\) \(2\) \(q+(3-3\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
144.3.q.b \(4\) \(3.924\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-3\) \(9\) \(1\) \(q+(-1+\beta _{3})q^{3}+(4-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
144.3.q.c \(4\) \(3.924\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(-18\) \(-2\) \(q+(1-2\beta _{1}-\beta _{3})q^{3}+(-3-3\beta _{1})q^{5}+\cdots\)
144.3.q.d \(4\) \(3.924\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(12\) \(6\) \(6\) \(q+3q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
144.3.q.e \(8\) \(3.924\) 8.0.\(\cdots\).9 None \(0\) \(-10\) \(-6\) \(-6\) \(q+(-1+\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)