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Properties

Label 2.72.a
Level $2$
Weight $72$
Character orbit 2.a
Rep. character $\chi_{2}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $2$
Sturm bound $18$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2 \)
Weight: \( k \) \(=\) \( 72 \)
Character orbit: \([\chi]\) \(=\) 2.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{72}(\Gamma_0(2))\).

Total New Old
Modular forms 19 5 14
Cusp forms 17 5 12
Eisenstein series 2 0 2

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

\(2\)Dim
\(+\)\(3\)
\(-\)\(2\)

Trace form

\( 5 q - 34359738368 q^{2} - 70\!\cdots\!88 q^{3} + 59\!\cdots\!20 q^{4} + 87\!\cdots\!50 q^{5} - 25\!\cdots\!80 q^{6} - 97\!\cdots\!24 q^{7} - 40\!\cdots\!32 q^{8} - 10\!\cdots\!15 q^{9} - 25\!\cdots\!00 q^{10}+ \cdots + 12\!\cdots\!20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{72}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
2.72.a.a 2.a 1.a $2$ $63.849$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.72.a.a \(68719476736\) \(-73\!\cdots\!24\) \(40\!\cdots\!00\) \(-29\!\cdots\!52\) $-$ $\mathrm{SU}(2)$ \(q+2^{35}q^{2}+(-36645276287423412+\cdots)q^{3}+\cdots\)
2.72.a.b 2.a 1.a $3$ $63.849$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 2.72.a.b \(-103079215104\) \(23\!\cdots\!36\) \(47\!\cdots\!50\) \(-68\!\cdots\!72\) $+$ $\mathrm{SU}(2)$ \(q-2^{35}q^{2}+(787523430902412+\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{72}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{72}^{\mathrm{old}}(\Gamma_0(2)) \simeq \) \(S_{72}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)