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Properties

Label 1025.2.a
Level $1025$
Weight $2$
Character orbit 1025.a
Rep. character $\chi_{1025}(1,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $16$
Sturm bound $210$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1025 = 5^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1025.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(210\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1025))\).

Total New Old
Modular forms 110 64 46
Cusp forms 99 64 35
Eisenstein series 11 0 11

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

\(5\)\(41\)FrickeDim
\(+\)\(+\)$+$\(13\)
\(+\)\(-\)$-$\(17\)
\(-\)\(+\)$-$\(21\)
\(-\)\(-\)$+$\(13\)
Plus space\(+\)\(26\)
Minus space\(-\)\(38\)

Trace form

\( 64 q + 2 q^{2} + 64 q^{4} - 6 q^{6} + 2 q^{7} + 6 q^{8} + 60 q^{9} + O(q^{10}) \) \( 64 q + 2 q^{2} + 64 q^{4} - 6 q^{6} + 2 q^{7} + 6 q^{8} + 60 q^{9} - 6 q^{11} + 8 q^{12} + 12 q^{13} + 4 q^{14} + 64 q^{16} + 8 q^{17} + 6 q^{18} + 4 q^{19} + 20 q^{21} + 4 q^{22} - 8 q^{23} - 38 q^{24} - 28 q^{26} - 18 q^{27} - 2 q^{28} + 4 q^{29} + 14 q^{32} - 16 q^{33} - 56 q^{34} + 28 q^{36} + 20 q^{37} - 34 q^{38} - 8 q^{39} - 4 q^{41} + 28 q^{42} + 4 q^{43} - 14 q^{44} + 24 q^{46} + 8 q^{47} - 4 q^{48} + 76 q^{49} - 28 q^{51} + 32 q^{52} + 8 q^{53} - 22 q^{54} + 8 q^{56} - 8 q^{57} - 36 q^{58} - 20 q^{59} + 8 q^{61} - 28 q^{62} + 40 q^{63} + 52 q^{64} - 28 q^{66} + 22 q^{67} + 20 q^{68} + 16 q^{69} - 20 q^{71} + 54 q^{72} - 16 q^{73} + 20 q^{74} + 20 q^{76} + 4 q^{77} - 72 q^{78} - 4 q^{79} + 32 q^{81} + 2 q^{82} - 12 q^{83} + 16 q^{84} + 16 q^{86} - 36 q^{87} + 28 q^{88} + 28 q^{89} + 28 q^{91} - 20 q^{92} + 14 q^{94} - 14 q^{96} - 4 q^{97} - 22 q^{98} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1025))\) 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 41
1025.2.a.a 1025.a 1.a $1$ $8.185$ \(\Q\) None \(-1\) \(-2\) \(0\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}+2q^{6}-2q^{7}+3q^{8}+\cdots\)
1025.2.a.b 1025.a 1.a $1$ $8.185$ \(\Q\) None \(1\) \(-2\) \(0\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}-q^{4}-2q^{6}-2q^{7}-3q^{8}+\cdots\)
1025.2.a.c 1025.a 1.a $1$ $8.185$ \(\Q\) None \(1\) \(0\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+4q^{7}-3q^{8}-3q^{9}+2q^{13}+\cdots\)
1025.2.a.d 1025.a 1.a $2$ $8.185$ \(\Q(\sqrt{13}) \) None \(-1\) \(-1\) \(0\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-\beta q^{3}+(1+\beta )q^{4}+(3+\beta )q^{6}+\cdots\)
1025.2.a.e 1025.a 1.a $2$ $8.185$ \(\Q(\sqrt{13}) \) None \(1\) \(1\) \(0\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+\beta q^{3}+(1+\beta )q^{4}+(3+\beta )q^{6}+\cdots\)
1025.2.a.f 1025.a 1.a $2$ $8.185$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
1025.2.a.g 1025.a 1.a $2$ $8.185$ \(\Q(\sqrt{13}) \) None \(1\) \(6\) \(0\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+3q^{3}+(1+\beta )q^{4}+3\beta q^{6}+\cdots\)
1025.2.a.h 1025.a 1.a $3$ $8.185$ 3.3.229.1 None \(-2\) \(-2\) \(0\) \(9\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\cdots\)
1025.2.a.i 1025.a 1.a $3$ $8.185$ 3.3.229.1 None \(0\) \(-2\) \(0\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1025.2.a.j 1025.a 1.a $3$ $8.185$ 3.3.148.1 None \(1\) \(0\) \(0\) \(-6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{2}-\beta _{2}q^{3}+(1+2\beta _{1})q^{4}+\cdots\)
1025.2.a.k 1025.a 1.a $5$ $8.185$ 5.5.313905.1 None \(0\) \(-4\) \(0\) \(-11\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}+(-1+\beta _{1}+\beta _{4})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
1025.2.a.l 1025.a 1.a $5$ $8.185$ 5.5.313905.1 None \(0\) \(4\) \(0\) \(11\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+(1-\beta _{1}-\beta _{4})q^{3}+(2\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1025.2.a.m 1025.a 1.a $6$ $8.185$ 6.6.3356224.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{6}+\cdots\)
1025.2.a.n 1025.a 1.a $7$ $8.185$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(-3\) \(0\) \(-14\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1025.2.a.o 1025.a 1.a $7$ $8.185$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(3\) \(3\) \(0\) \(14\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1025.2.a.p 1025.a 1.a $14$ $8.185$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(2+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(205))\)\(^{\oplus 2}\)