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Properties

Label 72.21.b
Level $72$
Weight $21$
Character orbit 72.b
Rep. character $\chi_{72}(19,\cdot)$
Character field $\Q$
Dimension $99$
Newform subspaces $4$
Sturm bound $252$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 21 \)
Character orbit: \([\chi]\) \(=\) 72.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(252\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(72, [\chi])\).

Total New Old
Modular forms 244 101 143
Cusp forms 236 99 137
Eisenstein series 8 2 6

Trace form

\( 99 q + 628 q^{2} - 267504 q^{4} + 609676444 q^{8} + O(q^{10}) \) \( 99 q + 628 q^{2} - 267504 q^{4} + 609676444 q^{8} - 10300080972 q^{10} - 14520628702 q^{11} + 347346537852 q^{14} + 3184617175248 q^{16} + 990389375402 q^{17} + 1375336086078 q^{19} - 16712772648648 q^{20} + 35786555301372 q^{22} - 1826238951618285 q^{25} + 169480344502272 q^{26} + 483694274694696 q^{28} + 3003613602435448 q^{32} + 1181918888641440 q^{34} + 3234393426905664 q^{35} - 21464478253103428 q^{38} - 59241470432225400 q^{40} - 2320164587283094 q^{41} - 34061137878160098 q^{43} - 38995922279897272 q^{44} - 59994246611399592 q^{46} - 1035109767928302525 q^{49} + 134551905327436156 q^{50} - 194020495051695936 q^{52} - 97204960107400152 q^{56} - 1140184757694411708 q^{58} + 1954151757601224098 q^{59} - 1607493854454198444 q^{62} - 1755455458389329808 q^{64} + 1574962450473910464 q^{65} + 1773610782729036030 q^{67} - 7860075384249332344 q^{68} + 9306089451940535112 q^{70} + 4497851542813262598 q^{73} + 30820581065840354328 q^{74} + 20783302310026584648 q^{76} + 56304248333026034208 q^{80} - 37586343012509615880 q^{82} + 10452525070055080322 q^{83} - 18356698016612978740 q^{86} + 17872718167235001168 q^{88} + 43617150548200737482 q^{89} - 15970522797644366976 q^{91} + 64406406827025718944 q^{92} + 7351803603366172248 q^{94} - 12927415363175728026 q^{97} - 64399653240512616308 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{21}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.21.b.a 72.b 8.d $1$ $182.530$ \(\Q\) \(\Q(\sqrt{-2}) \) \(-1024\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{10}q^{2}+2^{20}q^{4}-2^{30}q^{8}+42383023726q^{11}+\cdots\)
72.21.b.b 72.b 8.d $18$ $182.530$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(398\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(22+\beta _{1})q^{2}+(40275+21\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
72.21.b.c 72.b 8.d $40$ $182.530$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
72.21.b.d 72.b 8.d $40$ $182.530$ None \(1254\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{21}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{21}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{21}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)