Properties

Label 72.4.a
Level $72$
Weight $4$
Character orbit 72.a
Rep. character $\chi_{72}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $4$
Sturm bound $48$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 72.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(72))\).

Total New Old
Modular forms 44 4 40
Cusp forms 28 4 24
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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(2\)

Trace form

\( 4 q - 12 q^{5} - 24 q^{7} + O(q^{10}) \) \( 4 q - 12 q^{5} - 24 q^{7} + 72 q^{11} + 64 q^{13} - 132 q^{17} - 136 q^{19} + 48 q^{23} + 212 q^{25} - 60 q^{29} - 40 q^{31} + 384 q^{35} - 168 q^{37} - 84 q^{41} - 344 q^{43} - 768 q^{47} + 68 q^{49} + 372 q^{53} + 1744 q^{55} + 72 q^{59} - 584 q^{61} + 1080 q^{65} - 1240 q^{67} - 1584 q^{71} - 2048 q^{73} + 384 q^{77} + 1528 q^{79} + 1272 q^{83} + 2072 q^{85} - 468 q^{89} + 912 q^{91} - 1200 q^{95} + 800 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(72))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
72.4.a.a $1$ $4.248$ \(\Q\) None \(0\) \(0\) \(-16\) \(-12\) $-$ $+$ \(q-2^{4}q^{5}-12q^{7}-2^{6}q^{11}+58q^{13}+\cdots\)
72.4.a.b $1$ $4.248$ \(\Q\) None \(0\) \(0\) \(-14\) \(-24\) $+$ $-$ \(q-14q^{5}-24q^{7}+28q^{11}-74q^{13}+\cdots\)
72.4.a.c $1$ $4.248$ \(\Q\) None \(0\) \(0\) \(2\) \(24\) $-$ $-$ \(q+2q^{5}+24q^{7}+44q^{11}+22q^{13}+\cdots\)
72.4.a.d $1$ $4.248$ \(\Q\) None \(0\) \(0\) \(16\) \(-12\) $+$ $+$ \(q+2^{4}q^{5}-12q^{7}+2^{6}q^{11}+58q^{13}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(72))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(72)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)