Properties

Label 25.20.a
Level $25$
Weight $20$
Character orbit 25.a
Rep. character $\chi_{25}(1,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $6$
Sturm bound $50$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 20 \)
Character orbit: \([\chi]\) \(=\) 25.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(50\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(25))\).

Total New Old
Modular forms 51 31 20
Cusp forms 45 28 17
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
\(+\)\(14\)
\(-\)\(14\)

Trace form

\( 28 q + 970 q^{2} + 19720 q^{3} + 6141494 q^{4} - 40954614 q^{6} - 142193400 q^{7} + 816090840 q^{8} + 9935728536 q^{9} + O(q^{10}) \) \( 28 q + 970 q^{2} + 19720 q^{3} + 6141494 q^{4} - 40954614 q^{6} - 142193400 q^{7} + 816090840 q^{8} + 9935728536 q^{9} - 2805942024 q^{11} - 18245073760 q^{12} + 20396561440 q^{13} - 17251389492 q^{14} + 293381581458 q^{16} - 1161361765040 q^{17} + 5169226367170 q^{18} - 1066175275080 q^{19} + 4522145650536 q^{21} - 842554327160 q^{22} + 8444542907160 q^{23} + 16670576216910 q^{24} - 44281870791684 q^{26} + 103354481139760 q^{27} - 173263546523760 q^{28} - 23859533793120 q^{29} + 542839477027616 q^{31} + 140449949815520 q^{32} - 304460044658560 q^{33} - 170151992572442 q^{34} - 121465785494472 q^{36} + 548534964927680 q^{37} + 4402115792501560 q^{38} - 2322461781413328 q^{39} + 2833108880025036 q^{41} + 8663243061141360 q^{42} - 6152107648124600 q^{43} - 9081339520497102 q^{44} + 5026825645108196 q^{46} + 6958662792612040 q^{47} - 35814593101171840 q^{48} + 13102346233318204 q^{49} - 12665906038629864 q^{51} + 117331307113687400 q^{52} - 31509915857898080 q^{53} - 143998723252829730 q^{54} - 59046366894460020 q^{56} + 130495874587397920 q^{57} + 34947707573082140 q^{58} - 206257711529669040 q^{59} - 21185962058303224 q^{61} + 709003452330212640 q^{62} - 228966464348980920 q^{63} - 582470028678408606 q^{64} + 224183995406111562 q^{66} + 1344364627530260760 q^{67} - 1824774797555487880 q^{68} - 2209791666365299368 q^{69} + 360207894777032496 q^{71} + 5817047258346922680 q^{72} - 1487179106046133040 q^{73} - 1864522939007811192 q^{74} - 936822560107158590 q^{76} + 4178778364212436800 q^{77} - 1379072900750630800 q^{78} - 4710105261483552720 q^{79} + 4343864762608688028 q^{81} + 10304283006551233940 q^{82} + 1188924209264546280 q^{83} - 9130530692225718972 q^{84} + 1627510310673204456 q^{86} + 5710525713787114480 q^{87} - 5522129837295258720 q^{88} - 5411658553715966460 q^{89} - 7543194010449168784 q^{91} + 6223363374460456560 q^{92} - 10929854014886110560 q^{93} + 10856112763709789008 q^{94} - 14201863345467368034 q^{96} - 2422636743465831760 q^{97} - 12166625949247409590 q^{98} + 6756380583760400112 q^{99} + O(q^{100}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(25))\) 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
25.20.a.a 25.a 1.a $1$ $57.204$ \(\Q\) None \(-456\) \(-50652\) \(0\) \(16917544\) $+$ $\mathrm{SU}(2)$ \(q-456q^{2}-50652q^{3}-316352q^{4}+\cdots\)
25.20.a.b 25.a 1.a $3$ $57.204$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(1006\) \(73452\) \(0\) \(54910456\) $+$ $\mathrm{SU}(2)$ \(q+(335-\beta _{1})q^{2}+(24478-18\beta _{1}+13\beta _{2})q^{3}+\cdots\)
25.20.a.c 25.a 1.a $4$ $57.204$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(420\) \(-3080\) \(0\) \(-214021400\) $+$ $\mathrm{SU}(2)$ \(q+(105+\beta _{1})q^{2}+(-770-14\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
25.20.a.d 25.a 1.a $6$ $57.204$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-55\) \(-4180\) \(0\) \(-194109400\) $-$ $\mathrm{SU}(2)$ \(q+(-9-\beta _{1})q^{2}+(-698+8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
25.20.a.e 25.a 1.a $6$ $57.204$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(55\) \(4180\) \(0\) \(194109400\) $+$ $\mathrm{SU}(2)$ \(q+(9+\beta _{1})q^{2}+(698-8\beta _{1}-\beta _{2})q^{3}+\cdots\)
25.20.a.f 25.a 1.a $8$ $57.204$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(202593+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)