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Properties

Label 25.9.f
Level $25$
Weight $9$
Character orbit 25.f
Rep. character $\chi_{25}(2,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $152$
Newform subspaces $1$
Sturm bound $22$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 25.f (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(25, [\chi])\).

Total New Old
Modular forms 168 168 0
Cusp forms 152 152 0
Eisenstein series 16 16 0

Trace form

\( 152 q - 8 q^{2} + 62 q^{3} - 10 q^{4} - 230 q^{5} - 6 q^{6} + 2342 q^{7} + 8210 q^{8} - 10 q^{9} + O(q^{10}) \) \( 152 q - 8 q^{2} + 62 q^{3} - 10 q^{4} - 230 q^{5} - 6 q^{6} + 2342 q^{7} + 8210 q^{8} - 10 q^{9} - 30880 q^{10} - 6 q^{11} + 45902 q^{12} + 119132 q^{13} - 10 q^{14} - 241450 q^{15} + 524282 q^{16} - 105158 q^{17} + 454052 q^{18} + 718890 q^{19} + 340370 q^{20} - 6 q^{21} - 1986746 q^{22} - 899198 q^{23} + 2032310 q^{25} - 913936 q^{26} + 1904300 q^{27} - 998002 q^{28} - 1956910 q^{29} - 4500490 q^{30} - 6 q^{31} - 3033938 q^{32} + 1003994 q^{33} + 10303990 q^{34} + 4124560 q^{35} - 8100358 q^{36} + 9534392 q^{37} - 14259280 q^{38} - 22510410 q^{39} - 4123060 q^{40} - 4374726 q^{41} + 52199634 q^{42} + 13583342 q^{43} - 2138860 q^{44} - 33978380 q^{45} - 6 q^{46} - 11197058 q^{47} - 32869688 q^{48} + 13239250 q^{50} - 16 q^{51} + 93509212 q^{52} + 53717512 q^{53} + 57025140 q^{54} - 14642290 q^{55} - 262150 q^{56} - 93310490 q^{57} - 97437640 q^{58} + 24222740 q^{59} - 66375070 q^{60} - 18369126 q^{61} + 6782124 q^{62} + 96012652 q^{63} + 112817140 q^{64} + 89469970 q^{65} + 6718458 q^{66} + 74549142 q^{67} - 62262702 q^{68} - 128418860 q^{69} - 177099410 q^{70} + 60703854 q^{71} - 444425220 q^{72} - 171988248 q^{73} + 257329110 q^{75} - 262160 q^{76} + 292751454 q^{77} + 385000804 q^{78} + 138506190 q^{79} + 245270230 q^{80} + 110809772 q^{81} - 73650066 q^{82} - 663197528 q^{83} - 1517250010 q^{84} - 616093620 q^{85} - 6 q^{86} + 494144820 q^{87} + 1287340030 q^{88} + 1051406240 q^{89} + 1480613390 q^{90} - 6 q^{91} - 461835158 q^{92} - 908140736 q^{93} - 1160168810 q^{94} - 920404690 q^{95} + 172437534 q^{96} - 732746208 q^{97} - 167741852 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.9.f.a 25.f 25.f $152$ $10.184$ None \(-8\) \(62\) \(-230\) \(2342\) $\mathrm{SU}(2)[C_{20}]$