Properties

Label 72.6.a
Level $72$
Weight $6$
Character orbit 72.a
Rep. character $\chi_{72}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $6$
Sturm bound $72$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 72.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(72\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(72))\).

Total New Old
Modular forms 68 6 62
Cusp forms 52 6 46
Eisenstein series 16 0 16

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(3\)

Trace form

\( 6 q - 24 q^{5} + 24 q^{7} + O(q^{10}) \) \( 6 q - 24 q^{5} + 24 q^{7} - 144 q^{11} - 36 q^{13} + 1464 q^{17} - 192 q^{19} - 5088 q^{23} - 1326 q^{25} + 13704 q^{29} + 6840 q^{31} - 28032 q^{35} - 10716 q^{37} + 32088 q^{41} + 10848 q^{43} - 26880 q^{47} - 7242 q^{49} + 53160 q^{53} - 6432 q^{55} - 68112 q^{59} - 7692 q^{61} - 3024 q^{65} + 27216 q^{67} + 64224 q^{71} + 37716 q^{73} - 34944 q^{77} - 32904 q^{79} - 9840 q^{83} - 47952 q^{85} - 104040 q^{89} - 25680 q^{91} + 355296 q^{95} + 20004 q^{97} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(72))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
72.6.a.a $1$ $11.548$ \(\Q\) None \(0\) \(0\) \(-94\) \(144\) $+$ $-$ \(q-94q^{5}+12^{2}q^{7}+380q^{11}+814q^{13}+\cdots\)
72.6.a.b $1$ $11.548$ \(\Q\) None \(0\) \(0\) \(-38\) \(120\) $-$ $-$ \(q-38q^{5}+120q^{7}-524q^{11}-962q^{13}+\cdots\)
72.6.a.c $1$ $11.548$ \(\Q\) None \(0\) \(0\) \(-16\) \(12\) $+$ $+$ \(q-2^{4}q^{5}+12q^{7}-448q^{11}-206q^{13}+\cdots\)
72.6.a.d $1$ $11.548$ \(\Q\) None \(0\) \(0\) \(16\) \(12\) $-$ $+$ \(q+2^{4}q^{5}+12q^{7}+448q^{11}-206q^{13}+\cdots\)
72.6.a.e $1$ $11.548$ \(\Q\) None \(0\) \(0\) \(34\) \(-240\) $-$ $-$ \(q+34q^{5}-240q^{7}+124q^{11}+46q^{13}+\cdots\)
72.6.a.f $1$ $11.548$ \(\Q\) None \(0\) \(0\) \(74\) \(-24\) $+$ $-$ \(q+74q^{5}-24q^{7}-124q^{11}+478q^{13}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(72))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(72)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)