Properties

Label 72.3.m
Level $72$
Weight $3$
Character orbit 72.m
Rep. character $\chi_{72}(41,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 72.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(72, [\chi])\).

Total New Old
Modular forms 56 12 44
Cusp forms 40 12 28
Eisenstein series 16 0 16

Trace form

\( 12 q - 2 q^{3} + 14 q^{9} + O(q^{10}) \) \( 12 q - 2 q^{3} + 14 q^{9} + 18 q^{11} - 8 q^{15} + 12 q^{19} - 36 q^{21} - 72 q^{23} + 30 q^{25} - 128 q^{27} - 108 q^{29} + 24 q^{31} - 50 q^{33} + 124 q^{39} + 126 q^{41} - 18 q^{43} + 260 q^{45} + 324 q^{47} - 18 q^{49} + 170 q^{51} - 24 q^{55} - 202 q^{57} - 126 q^{59} - 48 q^{61} - 264 q^{63} - 432 q^{65} - 42 q^{67} - 104 q^{69} - 36 q^{73} + 266 q^{75} + 504 q^{77} - 60 q^{79} + 518 q^{81} + 180 q^{83} - 48 q^{85} - 36 q^{87} - 192 q^{91} - 352 q^{93} - 828 q^{95} + 6 q^{97} - 796 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.3.m.a 72.m 9.d $4$ $1.962$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(-12\) \(6\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q-3q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots\)
72.3.m.b 72.m 9.d $8$ $1.962$ 8.0.\(\cdots\).9 None \(0\) \(10\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

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