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Properties

Label 25.26.a
Level $25$
Weight $26$
Character orbit 25.a
Rep. character $\chi_{25}(1,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $6$
Sturm bound $65$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 25.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(65\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(25))\).

Total New Old
Modular forms 65 41 24
Cusp forms 59 38 21
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
\(+\)\(18\)
\(-\)\(20\)

Trace form

\( 38 q + 4050 q^{2} + 368200 q^{3} + 656474966 q^{4} - 7911669174 q^{6} - 45623726000 q^{7} + 97860857400 q^{8} + 11205302006334 q^{9} + O(q^{10}) \) \( 38 q + 4050 q^{2} + 368200 q^{3} + 656474966 q^{4} - 7911669174 q^{6} - 45623726000 q^{7} + 97860857400 q^{8} + 11205302006334 q^{9} + 25385924677176 q^{11} + 61853234711600 q^{12} - 138624117967100 q^{13} + 61807333992732 q^{14} + 10509631111776338 q^{16} - 321851708378100 q^{17} - 153265087690550 q^{18} + 25255586189979400 q^{19} + 44693765765710176 q^{21} + 24668707441704600 q^{22} - 229735197530348400 q^{23} - 600235677858102450 q^{24} + 2187574751192468076 q^{26} + 292278441455052400 q^{27} - 6149313968883965600 q^{28} + 3271640166579197700 q^{29} + 11085095416138257376 q^{31} + 17643160357674040800 q^{32} - 19847220889839241600 q^{33} - 19426198535789220618 q^{34} + 255905747767598702088 q^{36} - 29457504733263536300 q^{37} - 60808929521013725400 q^{38} - 53427163883005798032 q^{39} - 229317565381125689124 q^{41} - 197411449643133429600 q^{42} + 1020158421744100399000 q^{43} + 1522762442298781182882 q^{44} - 2495742253188144170124 q^{46} - 1216080359141727902400 q^{47} + 216021901924809041600 q^{48} + 8516600990625407169366 q^{49} + 8074749458122610918976 q^{51} + 2619173896302294241000 q^{52} - 4591897424783775132300 q^{53} - 17449887283282583810850 q^{54} + 4684912887182366850300 q^{56} - 7654732572721183143200 q^{57} - 19541697234710019632100 q^{58} + 33696406609177883250600 q^{59} + 45255667979530593003076 q^{61} + 3593185236875296137600 q^{62} - 3204436761153068317200 q^{63} + 262152601553906134793666 q^{64} - 320073958311104877823398 q^{66} - 82913208208814259188600 q^{67} + 184945344989415762130200 q^{68} + 177457957901464795959168 q^{69} + 67376702764651119714576 q^{71} - 649069131978335017525800 q^{72} + 535702643708815564467100 q^{73} + 560920634979423755002632 q^{74} + 746313406908655026432850 q^{76} + 172657581938287596972000 q^{77} - 821715793073046492178000 q^{78} - 2129584731949575532820000 q^{79} + 4990269436424306183414838 q^{81} - 1052703082177634243889900 q^{82} - 945347188713817021774200 q^{83} + 6783485256757421868068532 q^{84} - 7647642124930964622370824 q^{86} - 5862014826548114783166800 q^{87} + 4188943315677198128944800 q^{88} - 7271791578251707776012900 q^{89} - 2484810477712356667918624 q^{91} - 16377535913950776898821600 q^{92} + 6620138971904950429922400 q^{93} + 9706504887209786121749232 q^{94} - 4221323364997156864574274 q^{96} - 39981328862027310267566900 q^{97} + 46088911635828195978482850 q^{98} + 57577797455355907752856968 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(25))\) 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
25.26.a.a 25.a 1.a $1$ $98.999$ \(\Q\) None \(48\) \(195804\) \(0\) \(-39080597192\) $+$ $\mathrm{SU}(2)$ \(q+48q^{2}+195804q^{3}-33552128q^{4}+\cdots\)
25.26.a.b 25.a 1.a $4$ $98.999$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-600\) \(798600\) \(0\) \(48938107000\) $+$ $\mathrm{SU}(2)$ \(q+(-150+\beta _{1})q^{2}+(199650-17\beta _{1}+\cdots)q^{3}+\cdots\)
25.26.a.c 25.a 1.a $5$ $98.999$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(4602\) \(-626204\) \(0\) \(-55481235808\) $+$ $\mathrm{SU}(2)$ \(q+(920+\beta _{1})q^{2}+(-125251+5^{2}\beta _{1}+\cdots)q^{3}+\cdots\)
25.26.a.d 25.a 1.a $8$ $98.999$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8145\) \(-1149080\) \(0\) \(-75703856800\) $+$ $\mathrm{SU}(2)$ \(q+(-1018-\beta _{1})q^{2}+(-143638+26\beta _{1}+\cdots)q^{3}+\cdots\)
25.26.a.e 25.a 1.a $8$ $98.999$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8145\) \(1149080\) \(0\) \(75703856800\) $-$ $\mathrm{SU}(2)$ \(q+(1018+\beta _{1})q^{2}+(143638-26\beta _{1}+\cdots)q^{3}+\cdots\)
25.26.a.f 25.a 1.a $12$ $98.999$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(19\beta _{1}+\beta _{7})q^{3}+(13890962+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)