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Properties

Label 72.18.d
Level $72$
Weight $18$
Character orbit 72.d
Rep. character $\chi_{72}(37,\cdot)$
Character field $\Q$
Dimension $84$
Newform subspaces $4$
Sturm bound $216$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 18 \)
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: \(216\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(72, [\chi])\).

Total New Old
Modular forms 208 86 122
Cusp forms 200 84 116
Eisenstein series 8 2 6

Trace form

\( 84 q + 272 q^{2} + 82176 q^{4} + 11529600 q^{7} + 142709396 q^{8} + O(q^{10}) \) \( 84 q + 272 q^{2} + 82176 q^{4} + 11529600 q^{7} + 142709396 q^{8} + 224156604 q^{10} + 4350858884 q^{14} + 23189365008 q^{16} - 7489125596 q^{17} + 95639891672 q^{20} + 200006713836 q^{22} - 192886477448 q^{23} - 12185658994164 q^{25} + 1334772069776 q^{26} - 1002541245768 q^{28} - 9915712690704 q^{31} - 13235191668008 q^{32} - 4748642371464 q^{34} + 89628813800572 q^{38} - 104794961412360 q^{40} + 37985415033884 q^{41} - 345627213037320 q^{44} - 211595162097480 q^{46} + 99526928413464 q^{47} + 2796806598023364 q^{49} - 1118819604109576 q^{50} + 1842214144408896 q^{52} - 866241923650656 q^{55} + 2885031326220680 q^{56} - 63107786572260 q^{58} + 90666512176204 q^{62} + 3701843231351856 q^{64} + 2382936217543664 q^{65} - 2253115020979560 q^{68} - 7150535950630728 q^{70} - 9055172589304728 q^{71} + 5602948670836656 q^{73} - 1682974717024936 q^{74} - 440236862646312 q^{76} + 11630119140161280 q^{79} - 6448786028636736 q^{80} + 8081229852526416 q^{82} - 71114454595738084 q^{86} + 32845843587408048 q^{88} - 22728460153280332 q^{89} + 100469481460726560 q^{92} + 343946019443001192 q^{94} + 306081930612891280 q^{95} - 38808613862991840 q^{97} + 283865547788947464 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.18.d.a 72.d 8.b $2$ $131.920$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(18376324\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{7}\beta q^{2}-2^{17}q^{4}+493679\beta q^{5}+\cdots\)
72.18.d.b 72.d 8.b $16$ $131.920$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-270\) \(0\) \(0\) \(11529600\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-17-\beta _{1})q^{2}+(-1713+17\beta _{1}+\cdots)q^{4}+\cdots\)
72.18.d.c 72.d 8.b $32$ $131.920$ None \(0\) \(0\) \(0\) \(4682880\) $\mathrm{SU}(2)[C_{2}]$
72.18.d.d 72.d 8.b $34$ $131.920$ None \(542\) \(0\) \(0\) \(-23059204\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{18}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{18}^{\mathrm{old}}(72, [\chi]) \cong \)