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Properties

Label 25.10.d
Level $25$
Weight $10$
Character orbit 25.d
Rep. character $\chi_{25}(6,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $84$
Newform subspaces $1$
Sturm bound $25$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 10 \)
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: \(25\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(25, [\chi])\).

Total New Old
Modular forms 92 92 0
Cusp forms 84 84 0
Eisenstein series 8 8 0

Trace form

\( 84 q + 13 q^{2} - 151 q^{3} - 4867 q^{4} - 4610 q^{5} + 3613 q^{6} - 5952 q^{7} + 14380 q^{8} - 131668 q^{9} + O(q^{10}) \) \( 84 q + 13 q^{2} - 151 q^{3} - 4867 q^{4} - 4610 q^{5} + 3613 q^{6} - 5952 q^{7} + 14380 q^{8} - 131668 q^{9} + 1245 q^{10} + 47263 q^{11} + 151723 q^{12} + 909 q^{13} + 447871 q^{14} + 503025 q^{15} - 1967951 q^{16} - 152947 q^{17} - 1616016 q^{18} - 153395 q^{19} + 2977895 q^{20} + 1363008 q^{21} + 3660856 q^{22} + 4511089 q^{23} - 6818340 q^{24} - 9025280 q^{25} - 9688002 q^{26} - 3093085 q^{27} + 14115291 q^{28} + 712235 q^{29} + 21469035 q^{30} + 12756873 q^{31} - 32632362 q^{32} - 17130997 q^{33} + 7156541 q^{34} - 3060310 q^{35} + 6272269 q^{36} + 1644153 q^{37} + 6940445 q^{38} + 19494259 q^{39} - 57859470 q^{40} + 58333433 q^{41} - 37033219 q^{42} + 18427044 q^{43} + 125934396 q^{44} + 19423100 q^{45} - 105780007 q^{46} + 2767903 q^{47} + 5333194 q^{48} + 255772608 q^{49} - 206520835 q^{50} - 201283402 q^{51} + 28038408 q^{52} + 2054259 q^{53} + 565992175 q^{54} + 156884185 q^{55} - 416924310 q^{56} - 394535090 q^{57} - 740737250 q^{58} - 277069545 q^{59} + 567102810 q^{60} + 577284343 q^{61} - 46901544 q^{62} - 521860846 q^{63} - 1004145332 q^{64} - 1073691795 q^{65} + 1231043336 q^{66} + 154291493 q^{67} + 2959898126 q^{68} + 697866359 q^{69} + 857155880 q^{70} + 283347593 q^{71} - 724050335 q^{72} - 408433491 q^{73} - 2573796684 q^{74} - 159946705 q^{75} - 2429050880 q^{76} + 1412345336 q^{77} - 633477007 q^{78} + 994068455 q^{79} + 3123251580 q^{80} - 1664568886 q^{81} + 2667623986 q^{82} - 236717391 q^{83} - 600996364 q^{84} - 4229780835 q^{85} + 1092217503 q^{86} - 5688376045 q^{87} - 19076640 q^{88} + 1250480095 q^{89} + 3227628655 q^{90} + 1492351208 q^{91} - 4800624792 q^{92} + 4719812398 q^{93} + 4097235701 q^{94} + 5674562545 q^{95} - 1118596442 q^{96} - 4675486937 q^{97} - 4419748384 q^{98} - 3960658276 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.10.d.a 25.d 25.d $84$ $12.876$ None \(13\) \(-151\) \(-4610\) \(-5952\) $\mathrm{SU}(2)[C_{5}]$