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Properties

Label 25.7.f
Level $25$
Weight $7$
Character orbit 25.f
Rep. character $\chi_{25}(2,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $112$
Newform subspaces $1$
Sturm bound $17$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 7 \)
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: \(17\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(25, [\chi])\).

Total New Old
Modular forms 128 128 0
Cusp forms 112 112 0
Eisenstein series 16 16 0

Trace form

\( 112 q - 40 q^{3} - 10 q^{4} + 60 q^{5} - 6 q^{6} - 560 q^{7} - 1870 q^{8} - 10 q^{9} + O(q^{10}) \) \( 112 q - 40 q^{3} - 10 q^{4} + 60 q^{5} - 6 q^{6} - 560 q^{7} - 1870 q^{8} - 10 q^{9} + 4360 q^{10} - 6 q^{11} - 3490 q^{12} - 1970 q^{13} - 10 q^{14} + 80 q^{15} + 22522 q^{16} - 1210 q^{17} - 47740 q^{18} - 19210 q^{19} + 4290 q^{20} - 6 q^{21} + 116790 q^{22} + 68920 q^{23} - 83690 q^{25} + 32544 q^{26} - 147970 q^{27} - 191010 q^{28} - 24810 q^{29} + 128390 q^{30} - 6 q^{31} + 335470 q^{32} + 133250 q^{33} + 32990 q^{34} - 126400 q^{35} - 156358 q^{36} + 64990 q^{37} - 26320 q^{38} - 414810 q^{39} - 609460 q^{40} + 108554 q^{41} - 345630 q^{42} + 228280 q^{43} + 711540 q^{44} + 1026100 q^{45} - 6 q^{46} + 470440 q^{47} + 948520 q^{48} - 453750 q^{50} - 16 q^{51} - 1534020 q^{52} - 922770 q^{53} - 2582460 q^{54} - 1058910 q^{55} - 16390 q^{56} + 283510 q^{57} + 1902200 q^{58} + 2457990 q^{59} + 4557170 q^{60} - 388446 q^{61} - 686820 q^{62} - 2340440 q^{63} - 5040460 q^{64} - 1346350 q^{65} + 186618 q^{66} + 913000 q^{67} + 3094930 q^{68} + 2802790 q^{69} + 3485630 q^{70} - 758886 q^{71} + 3144300 q^{72} + 74290 q^{73} - 890640 q^{75} - 16400 q^{76} - 3146750 q^{77} - 5681900 q^{78} - 2289610 q^{79} - 6528330 q^{80} + 1577702 q^{81} + 1401150 q^{82} + 26480 q^{83} - 1650010 q^{84} - 3408980 q^{85} - 6 q^{86} - 735210 q^{87} + 2183870 q^{88} + 2906240 q^{89} + 3580070 q^{90} - 6 q^{91} + 1367450 q^{92} + 5352610 q^{93} + 14186390 q^{94} + 5887710 q^{95} - 1245186 q^{96} + 7532890 q^{97} + 5872380 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.7.f.a 25.f 25.f $112$ $5.751$ None \(0\) \(-40\) \(60\) \(-560\) $\mathrm{SU}(2)[C_{20}]$