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Properties

Label 48.11.l
Level $48$
Weight $11$
Character orbit 48.l
Rep. character $\chi_{48}(19,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $80$
Newform subspaces $1$
Sturm bound $88$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 48.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(88\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(48, [\chi])\).

Total New Old
Modular forms 164 80 84
Cusp forms 156 80 76
Eisenstein series 8 0 8

Trace form

\( 80 q + 2508 q^{4} - 138252 q^{8} + O(q^{10}) \) \( 80 q + 2508 q^{4} - 138252 q^{8} + 357224 q^{10} + 91808 q^{11} + 620136 q^{12} - 1519772 q^{14} - 1037024 q^{16} - 866052 q^{18} + 5107040 q^{19} - 4750000 q^{20} + 18397600 q^{22} + 16559488 q^{23} - 13107420 q^{24} + 48999500 q^{26} + 25399560 q^{28} + 59304608 q^{29} - 13407768 q^{30} + 149295520 q^{32} - 27029280 q^{34} - 68411424 q^{35} + 24013260 q^{36} + 189236256 q^{37} + 186228168 q^{38} + 355349808 q^{40} - 299089260 q^{42} - 360877792 q^{43} + 704131288 q^{44} + 450117416 q^{46} - 547753104 q^{48} + 3228288560 q^{49} - 232399196 q^{50} + 373209120 q^{51} + 1611170256 q^{52} - 1214144800 q^{53} - 95659380 q^{54} + 1427102464 q^{55} + 1023251488 q^{56} - 783581232 q^{58} - 1499085440 q^{59} - 2282417352 q^{60} - 1673280160 q^{61} + 2988847452 q^{62} + 5128320360 q^{64} - 2197430432 q^{65} + 3611203560 q^{66} + 6267013696 q^{67} - 7306925248 q^{68} - 1698239520 q^{69} + 8536315776 q^{70} - 15145776640 q^{71} - 1926965700 q^{72} + 9400896780 q^{74} + 5958608832 q^{75} - 5588761656 q^{76} + 1543017056 q^{77} - 12245360004 q^{78} - 6032827608 q^{80} - 30993639120 q^{81} + 7786450360 q^{82} - 14192131360 q^{83} + 11071288008 q^{84} - 4799500000 q^{85} - 20085853872 q^{86} - 13680934944 q^{88} - 5042154744 q^{90} - 27118234464 q^{91} - 3251386640 q^{92} + 10413195672 q^{94} + 1900104480 q^{96} + 22401405928 q^{98} + 1807056864 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.11.l.a 48.l 16.f $80$ $30.497$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{11}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)