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Properties

Label 25.6.d
Level $25$
Weight $6$
Character orbit 25.d
Rep. character $\chi_{25}(6,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $44$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 25.d (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(25, [\chi])\).

Total New Old
Modular forms 52 52 0
Cusp forms 44 44 0
Eisenstein series 8 8 0

Trace form

\( 44 q - 7 q^{2} - q^{3} - 147 q^{4} + 115 q^{5} + 133 q^{6} - 202 q^{7} - 500 q^{8} - 508 q^{9} + O(q^{10}) \) \( 44 q - 7 q^{2} - q^{3} - 147 q^{4} + 115 q^{5} + 133 q^{6} - 202 q^{7} - 500 q^{8} - 508 q^{9} - 55 q^{10} + 718 q^{11} - 437 q^{12} - 291 q^{13} - 689 q^{14} - 1125 q^{15} + 2609 q^{16} + 718 q^{17} + 8544 q^{18} + 4075 q^{19} + 1095 q^{20} - 2022 q^{21} - 3704 q^{22} - 1211 q^{23} - 19620 q^{24} - 2405 q^{25} - 17882 q^{26} + 9485 q^{27} + 9371 q^{28} + 14245 q^{29} + 14235 q^{30} - 8637 q^{31} + 30678 q^{32} - 21682 q^{33} - 5639 q^{34} - 36235 q^{35} + 31069 q^{36} - 50777 q^{37} + 6525 q^{38} + 7009 q^{39} - 3470 q^{40} + 5558 q^{41} + 19541 q^{42} + 61194 q^{43} + 26876 q^{44} + 76400 q^{45} + 14553 q^{46} - 46662 q^{47} - 150806 q^{48} - 24482 q^{49} - 21335 q^{50} - 121132 q^{51} + 72648 q^{52} - 93141 q^{53} + 18655 q^{54} + 11760 q^{55} + 47370 q^{56} + 292150 q^{57} - 38730 q^{58} + 47640 q^{59} + 26010 q^{60} - 26747 q^{61} - 46744 q^{62} + 78674 q^{63} + 31148 q^{64} - 61320 q^{65} + 45896 q^{66} + 123558 q^{67} + 123886 q^{68} - 117721 q^{69} + 12280 q^{70} + 110788 q^{71} - 586175 q^{72} - 146691 q^{73} - 179364 q^{74} - 108580 q^{75} - 269280 q^{76} - 153084 q^{77} + 405473 q^{78} - 54065 q^{79} - 360820 q^{80} + 277619 q^{81} - 353334 q^{82} - 54791 q^{83} + 374516 q^{84} + 764240 q^{85} - 74697 q^{86} + 229940 q^{87} + 997600 q^{88} + 217000 q^{89} - 21245 q^{90} - 181052 q^{91} + 801448 q^{92} - 380432 q^{93} - 165099 q^{94} - 61205 q^{95} + 925078 q^{96} - 562302 q^{97} - 982324 q^{98} - 680776 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.6.d.a 25.d 25.d $44$ $4.010$ None \(-7\) \(-1\) \(115\) \(-202\) $\mathrm{SU}(2)[C_{5}]$