Properties

Label 144.6.i
Level $144$
Weight $6$
Character orbit 144.i
Rep. character $\chi_{144}(49,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $58$
Newform subspaces $6$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 144.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(144, [\chi])\).

Total New Old
Modular forms 252 62 190
Cusp forms 228 58 170
Eisenstein series 24 4 20

Trace form

\( 58q + 2q^{3} - q^{5} + q^{7} + 20q^{9} + O(q^{10}) \) \( 58q + 2q^{3} - q^{5} + q^{7} + 20q^{9} + 727q^{11} - q^{13} - 1675q^{15} + 1000q^{17} + 4q^{19} - 579q^{21} - 3173q^{23} - 15626q^{25} + 6176q^{27} - 3981q^{29} - 1625q^{31} - 4973q^{33} - 35646q^{35} - 4q^{37} + 13265q^{39} + 2901q^{41} - 13865q^{43} - 8677q^{45} - 37935q^{47} - 55224q^{49} - 40742q^{51} - 4q^{53} - 6246q^{55} + 3758q^{57} + 55033q^{59} - q^{61} - 75807q^{63} - 5743q^{65} + q^{67} + 53005q^{69} + 23672q^{71} - 53632q^{73} + 57646q^{75} + 24885q^{77} + q^{79} - 106708q^{81} + 41693q^{83} - 3126q^{85} + 211455q^{87} + 207948q^{89} - 80758q^{91} + 164837q^{93} + 61748q^{95} - 58147q^{97} + 31729q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
144.6.i.a \(4\) \(23.095\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(-54\) \(-74\) \(q+(-3+6\beta _{1}-\beta _{3})q^{3}+(-3^{3}\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
144.6.i.b \(6\) \(23.095\) 6.0.\(\cdots\).3 None \(0\) \(-9\) \(-54\) \(132\) \(q+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-20+\cdots)q^{5}+\cdots\)
144.6.i.c \(8\) \(23.095\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(12\) \(78\) \(-28\) \(q+(3-3\beta _{1}+\beta _{4})q^{3}+(20\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
144.6.i.d \(10\) \(23.095\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-12\) \(-21\) \(-29\) \(q+(-2-2\beta _{1}+\beta _{3}+\beta _{4})q^{3}+(4\beta _{1}+\cdots)q^{5}+\cdots\)
144.6.i.e \(14\) \(23.095\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(25\) \(-93\) \(q+(-1+\beta _{2}+\beta _{4})q^{3}+(3-3\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
144.6.i.f \(16\) \(23.095\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(11\) \(25\) \(93\) \(q+(1-\beta _{1}-\beta _{6})q^{3}+(\beta _{2}+3\beta _{3}+\beta _{9}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)