Properties

Label 72.8.d
Level $72$
Weight $8$
Character orbit 72.d
Rep. character $\chi_{72}(37,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $4$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 72.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(72, [\chi])\).

Total New Old
Modular forms 88 36 52
Cusp forms 80 34 46
Eisenstein series 8 2 6

Trace form

\( 34 q + 8 q^{2} + 64 q^{4} - 688 q^{7} - 1084 q^{8} + O(q^{10}) \) \( 34 q + 8 q^{2} + 64 q^{4} - 688 q^{7} - 1084 q^{8} - 4564 q^{10} - 16684 q^{14} + 12304 q^{16} + 1456 q^{17} - 60328 q^{20} - 95188 q^{22} + 144712 q^{23} - 476814 q^{25} - 108016 q^{26} + 122456 q^{28} + 446768 q^{31} + 76888 q^{32} + 26280 q^{34} - 150308 q^{38} + 769880 q^{40} - 79960 q^{41} - 178920 q^{44} - 2502408 q^{46} - 510024 q^{47} + 3805218 q^{49} - 175984 q^{50} - 2774976 q^{52} + 920752 q^{55} + 825224 q^{56} - 702676 q^{58} + 1288636 q^{62} - 8665040 q^{64} + 1103984 q^{65} - 2872200 q^{68} + 4761112 q^{70} + 2424408 q^{71} + 4623692 q^{73} - 1275400 q^{74} - 2285256 q^{76} + 6990368 q^{79} - 1768704 q^{80} + 273024 q^{82} + 900764 q^{86} + 7449584 q^{88} + 9783536 q^{89} - 11674080 q^{92} - 22068984 q^{94} + 20789440 q^{95} + 2997452 q^{97} - 38047296 q^{98} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.8.d.a 72.d 8.b $2$ $22.492$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(-1508\) $\mathrm{U}(1)[D_{2}]$ \(q+4\beta q^{2}-2^{7}q^{4}+197\beta q^{5}-754q^{7}+\cdots\)
72.8.d.b 72.d 8.b $6$ $22.492$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-6\) \(0\) \(0\) \(-688\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{2}+(19+\beta _{1}+\beta _{3})q^{4}+\cdots\)
72.8.d.c 72.d 8.b $12$ $22.492$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(136\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(34+\beta _{3})q^{4}+(-3\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\)
72.8.d.d 72.d 8.b $14$ $22.492$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(14\) \(0\) \(0\) \(1372\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{2}+(-15+\beta _{1}-\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)