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Properties

Label 25.38.a
Level $25$
Weight $38$
Character orbit 25.a
Rep. character $\chi_{25}(1,\cdot)$
Character field $\Q$
Dimension $57$
Newform subspaces $6$
Sturm bound $95$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 38 \)
Character orbit: \([\chi]\) \(=\) 25.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(95\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{38}(\Gamma_0(25))\).

Total New Old
Modular forms 95 60 35
Cusp forms 89 57 32
Eisenstein series 6 3 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)Dim
\(+\)\(27\)
\(-\)\(30\)

Trace form

\( 57 q - 456542 q^{2} - 115256996 q^{3} + 3534209879574 q^{4} + 117577688711754 q^{6} - 8635604595791592 q^{7} + 17077038399488760 q^{8} + 7898794189110147981 q^{9} + O(q^{10}) \) \( 57 q - 456542 q^{2} - 115256996 q^{3} + 3534209879574 q^{4} + 117577688711754 q^{6} - 8635604595791592 q^{7} + 17077038399488760 q^{8} + 7898794189110147981 q^{9} + 22007045966410349604 q^{11} - 184086073191366736432 q^{12} + 206518035584543386614 q^{13} + 772160446463427145788 q^{14} + 228144324715081082088402 q^{16} - 79706342214129441373742 q^{17} - 19574766660617156637926 q^{18} + 230579441695241398681980 q^{19} - 1872971904289545730440816 q^{21} + 33432314833225467023355576 q^{22} - 22013298939511833198784776 q^{23} + 23486236415149971773997390 q^{24} + 367418256137347697696949324 q^{26} + 436232549602777832678994760 q^{27} - 2354925859378844490450574464 q^{28} - 976136035180530384106593930 q^{29} - 1912670293878042882122991216 q^{31} + 10908368732511762324855650528 q^{32} - 14452125340016602092802318912 q^{33} - 11227366486628375862784699242 q^{34} + 243195819767567522479961505192 q^{36} - 3272259550896901886209657842 q^{37} + 428202474303031256523917772040 q^{38} - 173903342440243232984097166968 q^{39} - 963785470712262927895711008726 q^{41} + 1478194965921511116220002685056 q^{42} - 2525658832683463805450598495756 q^{43} + 6948007156945898818363125784578 q^{44} + 22110711511841021250300458650644 q^{46} - 5074685748421048703319153461792 q^{47} - 84475633131993781823475162429376 q^{48} + 94530559869963390519037106495649 q^{49} - 13429019145696658692160110346656 q^{51} - 9626215104357302607941857625112 q^{52} - 102834450234395555745524812825346 q^{53} + 272116176001170387580952435582430 q^{54} + 244867157926772278337841884005980 q^{56} + 300544918653170097010444613824720 q^{57} - 2487092338307700178993403570666340 q^{58} + 659536790657270142932493810200940 q^{59} + 3928439817278051196864750288064854 q^{61} + 8063239788096899546852550150405696 q^{62} - 16538040206360268328936163142517176 q^{63} + 18514013341166925027401374846337154 q^{64} + 18786603926018201260037839290476538 q^{66} + 1790929371715497923961210871304508 q^{67} - 32732303063880128216172928443421864 q^{68} + 18204058731120441246321746610163392 q^{69} - 17678037632305775389420210207488456 q^{71} + 55334874431279867989594319088109080 q^{72} + 23804852066140286693744977567878474 q^{73} + 3476537333932509364271408805888648 q^{74} + 132517055189481985833349148565204210 q^{76} - 126263003565502945497567496180287024 q^{77} + 120577428194921472589677810793856048 q^{78} + 137425292862605017189717412924319120 q^{79} + 695801436238706794964141829679916337 q^{81} - 190039743865484656783219905756299244 q^{82} + 593752055649964052054944234661610684 q^{83} - 1451751821086464742272117111859192812 q^{84} - 1544550177302948293706307512284592616 q^{86} - 2505317110159115246723711373806660120 q^{87} + 7632190242398342017183582858682754720 q^{88} - 940896636722718488906569206206041590 q^{89} + 3119131295065690411882173156342140304 q^{91} + 264560759906766753275425734641054208 q^{92} + 3473430025172599136187112386538677648 q^{93} + 552519171047391304279503710429387568 q^{94} + 1380731946826607188554682634611778814 q^{96} + 2542421821383161443972961588037611058 q^{97} - 46184414782858346116004690182844701294 q^{98} + 31230759556286101671924675178269507132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{38}^{\mathrm{new}}(\Gamma_0(25))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
25.38.a.a 25.a 1.a $2$ $216.785$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(194400\) \(-13991400\) \(0\) \(34\!\cdots\!00\) $+$ $\mathrm{SU}(2)$ \(q+(97200-\beta )q^{2}+(-6995700+72\beta )q^{3}+\cdots\)
25.38.a.b 25.a 1.a $6$ $216.785$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-485440\) \(679418940\) \(0\) \(-16\!\cdots\!00\) $+$ $\mathrm{SU}(2)$ \(q+(-80907+\beta _{1})q^{2}+(113236553+\cdots)q^{3}+\cdots\)
25.38.a.c 25.a 1.a $7$ $216.785$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-165502\) \(-780684536\) \(0\) \(-10\!\cdots\!92\) $+$ $\mathrm{SU}(2)$ \(q+(-23643+\beta _{1})q^{2}+(-111526345+\cdots)q^{3}+\cdots\)
25.38.a.d 25.a 1.a $12$ $216.785$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-67745\) \(-724208180\) \(0\) \(22\!\cdots\!00\) $+$ $\mathrm{SU}(2)$ \(q+(-5645-\beta _{1})q^{2}+(-60350680+\cdots)q^{3}+\cdots\)
25.38.a.e 25.a 1.a $12$ $216.785$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(67745\) \(724208180\) \(0\) \(-22\!\cdots\!00\) $-$ $\mathrm{SU}(2)$ \(q+(5645+\beta _{1})q^{2}+(60350680+5\beta _{1}+\cdots)q^{3}+\cdots\)
25.38.a.f 25.a 1.a $18$ $216.785$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(61\beta _{1}-\beta _{10})q^{3}+(76582854812+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{38}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{38}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{38}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{38}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)