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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
25.6.d.a \(44\) \(4.010\) None \(-7\) \(-1\) \(115\) \(-202\)