↑

Properties

Label 24.28.f
Level $24$
Weight $28$
Character orbit 24.f
Rep. character $\chi_{24}(11,\cdot)$
Character field $\Q$
Dimension $106$
Newform subspaces $2$
Sturm bound $112$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 28 \)
Character orbit: \([\chi]\) \(=\) 24.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{28}(24, [\chi])\).

Total New Old
Modular forms 110 110 0
Cusp forms 106 106 0
Eisenstein series 4 4 0

Trace form

\( 106 q - 2 q^{3} + 118953412 q^{4} - 29615742008 q^{6} - 2 q^{9} + O(q^{10}) \) \( 106 q - 2 q^{3} + 118953412 q^{4} - 29615742008 q^{6} - 2 q^{9} - 11696046941304 q^{10} + 833046350880916 q^{12} + 90275072969320 q^{16} - 234338308101394376 q^{18} - 361273435637780380 q^{19} - 2716164181482802816 q^{22} - 3320436517261267640 q^{24} + 146031379699707031246 q^{25} + 16968274332320900026 q^{27} - 64802173230062700912 q^{28} + 121976691666319684176 q^{30} - 2632575711256057504 q^{33} + 109067432386588281968 q^{34} + 530142361225984950604 q^{36} - 7893933656518536719328 q^{40} + 11744252006007279620040 q^{42} - 14200115812612743847252 q^{43} - 36010569275877185639136 q^{46} - 178122222708366231496520 q^{48} - 825819634460874635230250 q^{49} + 62120836396250542956272 q^{51} - 442783254290529153653568 q^{52} + 411495469774191220854808 q^{54} - 275113126452436693837804 q^{57} + 430639113796083234682344 q^{58} + 2126303856333605132718000 q^{60} + 11162554382786085248008624 q^{64} - 18537552773258476852539160 q^{66} - 16791855426275982771219556 q^{67} - 29404244700669557820006864 q^{70} - 32677907530310337652297520 q^{72} + 6425348165429409878800532 q^{73} - 68365725821360739276484838 q^{75} + 6561606820671805224035480 q^{76} - 53289960447911890953260976 q^{78} - 31880826074766791642298758 q^{81} - 121391761928980436494476736 q^{82} - 154782558650154535863594240 q^{84} - 220967974220292151399000912 q^{88} + 853672785457912285624427304 q^{90} + 602709767970401640299590368 q^{91} + 2279573344482043094174236608 q^{94} + 2821951986727434061814868880 q^{96} - 1110522253821305274003465652 q^{97} + 2074549009847927035532477840 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{28}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.28.f.a 24.f 24.f $2$ $110.845$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) 24.28.f.a \(0\) \(-4360310\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{13}\beta q^{2}+(-2180155+1198441\beta )q^{3}+\cdots\)
24.28.f.b 24.f 24.f $104$ $110.845$ None 24.28.f.b \(0\) \(4360308\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$