Properties

Label 425.2.a
Level $425$
Weight $2$
Character orbit 425.a
Rep. character $\chi_{425}(1,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $10$
Sturm bound $90$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 425 = 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 425.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(90\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(425))\).

Total New Old
Modular forms 50 26 24
Cusp forms 39 26 13
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.

\(5\)\(17\)FrickeDim
\(+\)\(+\)$+$\(3\)
\(+\)\(-\)$-$\(9\)
\(-\)\(+\)$-$\(9\)
\(-\)\(-\)$+$\(5\)
Plus space\(+\)\(8\)
Minus space\(-\)\(18\)

Trace form

\( 26 q + 2 q^{2} + 30 q^{4} + 4 q^{7} + 6 q^{8} + 22 q^{9} + O(q^{10}) \) \( 26 q + 2 q^{2} + 30 q^{4} + 4 q^{7} + 6 q^{8} + 22 q^{9} - 4 q^{11} - 4 q^{12} + 8 q^{13} - 16 q^{14} + 38 q^{16} + 2 q^{17} - 2 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{22} - 36 q^{24} - 16 q^{26} + 12 q^{27} + 16 q^{28} - 8 q^{29} + 8 q^{31} - 6 q^{32} - 28 q^{33} - 2 q^{34} + 26 q^{36} + 12 q^{37} - 8 q^{38} + 8 q^{39} - 24 q^{41} - 4 q^{42} - 4 q^{43} + 20 q^{44} - 20 q^{47} + 24 q^{48} + 22 q^{49} - 4 q^{51} - 8 q^{52} - 20 q^{53} - 40 q^{54} - 44 q^{56} + 4 q^{58} + 8 q^{59} + 12 q^{61} - 4 q^{62} + 24 q^{63} + 54 q^{64} - 48 q^{66} + 20 q^{67} + 6 q^{68} + 8 q^{69} + 36 q^{71} + 2 q^{72} + 32 q^{73} - 48 q^{74} - 16 q^{76} - 4 q^{77} - 36 q^{78} + 40 q^{79} - 30 q^{81} - 20 q^{83} - 68 q^{84} - 24 q^{86} + 8 q^{87} - 28 q^{88} + 4 q^{89} + 48 q^{91} + 12 q^{92} + 28 q^{93} - 48 q^{94} - 152 q^{96} - 4 q^{97} + 38 q^{98} - 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(425))\) 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 17
425.2.a.a 425.a 1.a $1$ $3.394$ \(\Q\) None \(-1\) \(-2\) \(0\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}+2q^{6}+2q^{7}+3q^{8}+\cdots\)
425.2.a.b 425.a 1.a $1$ $3.394$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots\)
425.2.a.c 425.a 1.a $1$ $3.394$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots\)
425.2.a.d 425.a 1.a $1$ $3.394$ \(\Q\) None \(1\) \(0\) \(0\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{7}-3q^{8}-3q^{9}+2q^{13}+\cdots\)
425.2.a.e 425.a 1.a $2$ $3.394$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}+(-3-\beta )q^{6}+\cdots\)
425.2.a.f 425.a 1.a $2$ $3.394$ \(\Q(\sqrt{2}) \) None \(2\) \(4\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(2-\beta )q^{3}+(1+2\beta )q^{4}+\cdots\)
425.2.a.g 425.a 1.a $4$ $3.394$ 4.4.6224.1 None \(-2\) \(-4\) \(0\) \(-10\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}+(-1+\beta _{1})q^{3}+(1+\cdots)q^{4}+\cdots\)
425.2.a.h 425.a 1.a $4$ $3.394$ 4.4.6224.1 None \(2\) \(4\) \(0\) \(10\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
425.2.a.i 425.a 1.a $5$ $3.394$ 5.5.1893456.1 None \(-1\) \(1\) \(0\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(2+\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots\)
425.2.a.j 425.a 1.a $5$ $3.394$ 5.5.1893456.1 None \(1\) \(-1\) \(0\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(2+\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(425))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(425)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 2}\)