Properties

Label 3.25.b
Level 3
Weight 25
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 7
Newforms 2
Sturm bound 8
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 25 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{25}(3, [\chi])\).

Total New Old
Modular forms 9 9 0
Cusp forms 7 7 0
Eisenstein series 2 2 0

Trace form

\( 7q - 85401q^{3} - 46569584q^{4} - 2673890352q^{6} - 2131645522q^{7} - 508757413401q^{9} + O(q^{10}) \) \( 7q - 85401q^{3} - 46569584q^{4} - 2673890352q^{6} - 2131645522q^{7} - 508757413401q^{9} + 2770823311200q^{10} - 9576761394096q^{12} - 31824060862162q^{13} + 227151045057600q^{15} - 151860922193792q^{16} - 1227888881468640q^{18} + 1988533064931278q^{19} + 516727085313006q^{21} - 4132747004902560q^{22} + 79223562819483264q^{24} - 146670059787577625q^{25} - 3592764796415481q^{27} - 57692018929256032q^{28} + 1679034252186079200q^{30} - 2432070334989205906q^{31} + 7067811391497299520q^{33} - 15440589345121992576q^{34} + 27780257189026193040q^{36} - 19210795384095860242q^{37} + 47551592694661991406q^{39} - 121930725979226707200q^{40} + 209343891033396594720q^{42} - 194466917961721956082q^{43} + 311304965429932790400q^{45} - 346860905830754272704q^{46} + 200750182340220468864q^{48} - 66661435519971241515q^{49} - 479022139696737883392q^{51} + 575810995590114183968q^{52} - 1113391638534691344528q^{54} + 1679273232066520675200q^{55} - 3322862988741111600882q^{57} + 7395366373865537628960q^{58} - 14436777252623118393600q^{60} + 10189837827082476542894q^{61} - 9488937931815301905042q^{63} + 16464258977847379256320q^{64} - 5418873997530695523360q^{66} + 999942108302500933838q^{67} + 11943290073056639859072q^{69} - 55632387081854182017600q^{70} + 63773250138227244591360q^{72} - 27663264169543387325362q^{73} + 69399679398676353858375q^{75} - 73142881670934245711200q^{76} + 235720510135983845200800q^{78} - 344261156933687330285842q^{79} + 182492533768104250437447q^{81} - 272255725325320387035840q^{82} + 164265056607516829913376q^{84} + 319008824808936798988800q^{85} - 252430535429613815803200q^{87} + 160152458683551892335360q^{88} - 1246806301659161625597600q^{90} + 1325165683877806341550492q^{91} - 1188970608873583247379282q^{93} + 1979316836866080826257024q^{94} - 1420600675222724601424896q^{96} - 34528494773324481653362q^{97} - 1834460043482282449115520q^{99} + O(q^{100}) \)

Decomposition of \(S_{25}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.25.b.a \(1\) \(10.949\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(531441\) \(0\) \(-4119710398\) \(q+3^{12}q^{3}+2^{24}q^{4}-4119710398q^{7}+\cdots\)
3.25.b.b \(6\) \(10.949\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(-616842\) \(0\) \(1988064876\) \(q+\beta _{1}q^{2}+(-102807+2^{4}\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)