Properties

Label 25.36.a
Level $25$
Weight $36$
Character orbit 25.a
Rep. character $\chi_{25}(1,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $6$
Sturm bound $90$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 36 \)
Character orbit: \([\chi]\) \(=\) 25.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(90\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{36}(\Gamma_0(25))\).

Total New Old
Modular forms 91 57 34
Cusp forms 85 54 31
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
\(+\)\(26\)
\(-\)\(28\)

Trace form

\( 54 q + 270730 q^{2} + 78231280 q^{3} + 935983540022 q^{4} + 42846944162058 q^{6} + 688992159656000 q^{7} + 15391997172428760 q^{8} + 850205121918669678 q^{9} + O(q^{10}) \) \( 54 q + 270730 q^{2} + 78231280 q^{3} + 935983540022 q^{4} + 42846944162058 q^{6} + 688992159656000 q^{7} + 15391997172428760 q^{8} + 850205121918669678 q^{9} - 952390437530859792 q^{11} + 9813518506077078560 q^{12} - 13143141574485707740 q^{13} - 374746187767521240756 q^{14} + 13425699467187502711954 q^{16} - 314945430893663698460 q^{17} + 6696637491539907993730 q^{18} - 15783868278344920484800 q^{19} - 272328544566201157480392 q^{21} + 45897263003471302634760 q^{22} + 664031925272736046817040 q^{23} + 456415648190826963555150 q^{24} - 2556593092279767423509892 q^{26} - 20830776239159426646319760 q^{27} + 93539873776481840008946960 q^{28} + 107455020486875352340970100 q^{29} + 222347581603684636603155408 q^{31} + 697039368430562740148922080 q^{32} - 595428869724983735017693840 q^{33} + 426286111376493581715752294 q^{34} + 15235323282993420464632882104 q^{36} - 4763923746110408174112393580 q^{37} - 3351530043600312049921714760 q^{38} - 8434005843734311724465970144 q^{39} - 45493611922845898383781996692 q^{41} - 35759410074612106844893228560 q^{42} + 85605644508293556818067328400 q^{43} - 136832628125828450015360003406 q^{44} - 495043322500725562650407438492 q^{46} - 321782708014024084830348572240 q^{47} + 1055370468826627013416054547840 q^{48} + 3418478465895171648738666145022 q^{49} - 899693073579688566598942061592 q^{51} - 1379748562100115749254922767000 q^{52} + 3838910954047470346501675928980 q^{53} - 451981794253308564267561238050 q^{54} - 41204678038636163805539929638900 q^{56} - 14682079504073588758513565959520 q^{57} + 57863404786439745923608532920860 q^{58} + 36699860653205532066124786213800 q^{59} - 44468047531789657768492854771492 q^{61} + 2505867812743850034348754083360 q^{62} + 95289617300771277515196045449520 q^{63} + 125405997095592168718917660487522 q^{64} + 205817449906693196463385588197066 q^{66} - 136631377676152078708665300579760 q^{67} - 73277975429853314987233298198920 q^{68} - 131460809813850671185465551283944 q^{69} + 962704871962360115000228827425408 q^{71} + 581566266832622820900688788782520 q^{72} - 759725811798622070058497251908460 q^{73} - 49058777360997136304617335515256 q^{74} + 1861595477796918812676477787120450 q^{76} + 1978887731359262549785038594850800 q^{77} - 6995680107866969674905992493466000 q^{78} - 1710349774184532572078174862676000 q^{79} + 24605780550897678214163121051760254 q^{81} - 873025954931772563954719061740140 q^{82} - 4484262389679987927762531019606080 q^{83} + 422095746424198396619684474018244 q^{84} + 11046249016631404288579463279471208 q^{86} + 17159390433047068183225591725766720 q^{87} + 19999961627474872017844925189231520 q^{88} - 13167533859266546148322264702652700 q^{89} - 86928574053234081149094716885482192 q^{91} - 53154688372457139500227843564646160 q^{92} + 106962838426225265342118080994657360 q^{93} + 153276121330068053515297210795544144 q^{94} - 213604809014218803365016850008627042 q^{96} + 61475445032614458931462580425952660 q^{97} + 212248185203999672603048616285162890 q^{98} - 379299453425989850850662484616357944 q^{99} + O(q^{100}) \)

Decomposition of \(S_{36}^{\mathrm{new}}(\Gamma_0(25))\) 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
25.36.a.a 25.a 1.a $3$ $193.988$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-139656\) \(104875308\) \(0\) \(-87\!\cdots\!56\) $+$ $\mathrm{SU}(2)$ \(q+(-46552-\beta _{1})q^{2}+(34958436+\cdots)q^{3}+\cdots\)
25.36.a.b 25.a 1.a $5$ $193.988$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(459086\) \(257790672\) \(0\) \(67\!\cdots\!56\) $+$ $\mathrm{SU}(2)$ \(q+(91817-\beta _{1})q^{2}+(51558094-204\beta _{1}+\cdots)q^{3}+\cdots\)
25.36.a.c 25.a 1.a $6$ $193.988$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-48700\) \(-284434700\) \(0\) \(88\!\cdots\!00\) $+$ $\mathrm{SU}(2)$ \(q+(-8117-\beta _{1})q^{2}+(-47405712+\cdots)q^{3}+\cdots\)
25.36.a.d 25.a 1.a $12$ $193.988$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-8585\) \(271602340\) \(0\) \(46\!\cdots\!00\) $+$ $\mathrm{SU}(2)$ \(q+(-715-\beta _{1})q^{2}+(22633566-91\beta _{1}+\cdots)q^{3}+\cdots\)
25.36.a.e 25.a 1.a $12$ $193.988$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(8585\) \(-271602340\) \(0\) \(-46\!\cdots\!00\) $-$ $\mathrm{SU}(2)$ \(q+(715+\beta _{1})q^{2}+(-22633566+91\beta _{1}+\cdots)q^{3}+\cdots\)
25.36.a.f 25.a 1.a $16$ $193.988$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-98\beta _{1}+\beta _{9})q^{3}+(13178364041+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{36}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{36}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{36}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)