Properties

Label 72.2.i
Level $72$
Weight $2$
Character orbit 72.i
Rep. character $\chi_{72}(25,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 72.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(72, [\chi])\).

Total New Old
Modular forms 32 6 26
Cusp forms 16 6 10
Eisenstein series 16 0 16

Trace form

\( 6q + q^{3} + 2q^{5} - q^{9} + O(q^{10}) \) \( 6q + q^{3} + 2q^{5} - q^{9} - 7q^{11} - 14q^{15} - 14q^{17} + 6q^{19} - 12q^{21} - 4q^{23} - 3q^{25} + 16q^{27} + 12q^{29} - 6q^{31} + 13q^{33} + 36q^{35} + 34q^{39} + 9q^{41} - 9q^{43} + 2q^{45} - 9q^{49} - 19q^{51} - 16q^{53} - 12q^{55} - 13q^{57} - 25q^{59} - 6q^{61} - 18q^{63} + 14q^{65} - 3q^{67} + 22q^{69} - 8q^{71} - 18q^{73} - 19q^{75} + 12q^{77} + 6q^{79} + 11q^{81} - 26q^{83} + 12q^{85} - 24q^{87} - 12q^{89} + 12q^{91} - 10q^{93} + 16q^{95} + 21q^{97} + 20q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
72.2.i.a \(2\) \(0.575\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(3\) \(q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+3\zeta_{6}q^{7}+\cdots\)
72.2.i.b \(4\) \(0.575\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(1\) \(1\) \(-3\) \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

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