Properties

Label 425.4.a
Level $425$
Weight $4$
Character orbit 425.a
Rep. character $\chi_{425}(1,\cdot)$
Character field $\Q$
Dimension $76$
Newform subspaces $15$
Sturm bound $180$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 425 = 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 425.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(180\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(425))\).

Total New Old
Modular forms 142 76 66
Cusp forms 130 76 54
Eisenstein series 12 0 12

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.
\(+\)\(+\)\(+\)\(21\)
\(+\)\(-\)\(-\)\(15\)
\(-\)\(+\)\(-\)\(18\)
\(-\)\(-\)\(+\)\(22\)
Plus space\(+\)\(43\)
Minus space\(-\)\(33\)

Trace form

\( 76 q - 2 q^{2} + 4 q^{3} + 314 q^{4} - 10 q^{6} + 18 q^{7} + 66 q^{8} + 624 q^{9} + O(q^{10}) \) \( 76 q - 2 q^{2} + 4 q^{3} + 314 q^{4} - 10 q^{6} + 18 q^{7} + 66 q^{8} + 624 q^{9} + 92 q^{11} + 190 q^{12} + 20 q^{13} - 36 q^{14} + 1074 q^{16} - 34 q^{17} + 294 q^{18} - 36 q^{19} + 48 q^{21} - 150 q^{22} - 182 q^{23} + 354 q^{24} + 460 q^{26} - 476 q^{27} + 100 q^{28} - 214 q^{29} + 22 q^{31} + 766 q^{32} + 292 q^{33} + 68 q^{34} + 2050 q^{36} + 490 q^{37} - 1600 q^{38} + 828 q^{39} + 276 q^{41} - 220 q^{42} + 712 q^{43} - 1294 q^{44} + 464 q^{46} - 368 q^{47} + 962 q^{48} + 3868 q^{49} + 204 q^{51} - 268 q^{52} + 820 q^{53} - 980 q^{54} + 1744 q^{56} + 672 q^{57} + 2686 q^{58} - 328 q^{59} + 1534 q^{61} + 712 q^{62} - 2338 q^{63} + 4626 q^{64} - 732 q^{66} - 2500 q^{67} - 408 q^{68} - 5016 q^{69} - 650 q^{71} + 5882 q^{72} - 1848 q^{73} + 530 q^{74} - 1088 q^{76} - 592 q^{77} + 2424 q^{78} - 2362 q^{79} + 6824 q^{81} - 4420 q^{82} + 1560 q^{83} + 5556 q^{84} + 2540 q^{86} + 884 q^{87} - 90 q^{88} - 3096 q^{89} + 2432 q^{91} - 5268 q^{92} - 4152 q^{93} + 2440 q^{94} - 1578 q^{96} + 2180 q^{97} + 1122 q^{98} + 9168 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(425))\) 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
425.4.a.a 425.a 1.a $1$ $25.076$ \(\Q\) None \(-3\) \(-10\) \(0\) \(22\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{2}-10q^{3}+q^{4}+30q^{6}+22q^{7}+\cdots\)
425.4.a.b 425.a 1.a $1$ $25.076$ \(\Q\) None \(-3\) \(5\) \(0\) \(22\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{2}+5q^{3}+q^{4}-15q^{6}+22q^{7}+\cdots\)
425.4.a.c 425.a 1.a $1$ $25.076$ \(\Q\) None \(-3\) \(7\) \(0\) \(22\) $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+7q^{3}+q^{4}-21q^{6}+22q^{7}+\cdots\)
425.4.a.d 425.a 1.a $1$ $25.076$ \(\Q\) None \(3\) \(8\) \(0\) \(28\) $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{2}+8q^{3}+q^{4}+24q^{6}+28q^{7}+\cdots\)
425.4.a.e 425.a 1.a $2$ $25.076$ \(\Q(\sqrt{3}) \) None \(4\) \(2\) \(0\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{2}+(1+\beta )q^{3}+(-1+4\beta )q^{4}+\cdots\)
425.4.a.f 425.a 1.a $3$ $25.076$ 3.3.568.1 None \(-3\) \(-9\) \(0\) \(-34\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{2}+(-4+3\beta _{1}+\cdots)q^{3}+\cdots\)
425.4.a.g 425.a 1.a $3$ $25.076$ 3.3.2636.1 None \(-1\) \(-4\) \(0\) \(-22\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{2})q^{2}+(-2+\beta _{1}-2\beta _{2})q^{3}+\cdots\)
425.4.a.h 425.a 1.a $3$ $25.076$ 3.3.1304.1 None \(6\) \(4\) \(0\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta _{1})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(3+\cdots)q^{4}+\cdots\)
425.4.a.i 425.a 1.a $5$ $25.076$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-2\) \(1\) \(0\) \(-10\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+\beta _{2}q^{3}+(6-2\beta _{1}+\beta _{3})q^{4}+\cdots\)
425.4.a.j 425.a 1.a $6$ $25.076$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-1\) \(6\) \(0\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
425.4.a.k 425.a 1.a $6$ $25.076$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(1\) \(-6\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
425.4.a.l 425.a 1.a $10$ $25.076$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-1\) \(6\) \(0\) \(16\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{6})q^{3}+(6+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
425.4.a.m 425.a 1.a $10$ $25.076$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(1\) \(-6\) \(0\) \(-16\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{6})q^{3}+(6+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
425.4.a.n 425.a 1.a $12$ $25.076$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(-12\) \(0\) \(-70\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(4+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
425.4.a.o 425.a 1.a $12$ $25.076$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(12\) \(0\) \(70\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{4})q^{3}+(4+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(425))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(425)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 2}\)