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Properties

Label 425.3.u
Level $425$
Weight $3$
Character orbit 425.u
Rep. character $\chi_{425}(126,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $432$
Newform subspaces $6$
Sturm bound $135$
Trace bound $12$

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Defining parameters

Level: \( N \) \(=\) \( 425 = 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 425.u (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 6 \)
Sturm bound: \(135\)
Trace bound: \(12\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(425, [\chi])\).

Total New Old
Modular forms 768 480 288
Cusp forms 672 432 240
Eisenstein series 96 48 48

Trace form

\( 432 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 24 q^{6} + 8 q^{7} + 8 q^{8} + 8 q^{9} + O(q^{10}) \) \( 432 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 24 q^{6} + 8 q^{7} + 8 q^{8} + 8 q^{9} - 64 q^{11} + 104 q^{12} + 32 q^{13} + 40 q^{14} - 48 q^{18} - 16 q^{19} + 96 q^{21} - 88 q^{22} - 48 q^{23} - 328 q^{24} - 208 q^{26} + 152 q^{27} + 248 q^{28} + 248 q^{29} - 88 q^{31} + 16 q^{32} + 72 q^{34} + 200 q^{36} - 120 q^{37} - 96 q^{38} + 24 q^{39} - 288 q^{41} - 808 q^{42} - 120 q^{43} - 24 q^{44} + 312 q^{46} - 112 q^{47} + 96 q^{48} - 24 q^{49} - 56 q^{51} + 144 q^{52} - 256 q^{53} - 104 q^{54} - 64 q^{56} + 848 q^{57} - 752 q^{58} + 552 q^{59} + 88 q^{61} + 864 q^{62} - 688 q^{63} + 472 q^{64} - 80 q^{66} - 96 q^{68} - 416 q^{69} - 360 q^{71} - 1104 q^{72} - 72 q^{73} - 688 q^{74} - 1040 q^{76} - 696 q^{77} + 768 q^{78} - 536 q^{79} - 952 q^{81} - 728 q^{82} + 640 q^{83} - 1184 q^{86} + 824 q^{87} + 1224 q^{88} + 704 q^{89} - 328 q^{91} + 1656 q^{92} + 808 q^{93} + 1320 q^{94} + 848 q^{96} + 552 q^{97} + 920 q^{98} + 664 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(425, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
425.3.u.a 425.u 17.e $8$ $11.580$ \(\Q(\zeta_{16})\) None 17.3.e.b \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{16}]$ \(q+(\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{7})q^{2}+(-2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
425.3.u.b 425.u 17.e $8$ $11.580$ \(\Q(\zeta_{16})\) None 17.3.e.a \(8\) \(8\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
425.3.u.c 425.u 17.e $96$ $11.580$ None 425.3.u.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
425.3.u.d 425.u 17.e $96$ $11.580$ None 425.3.u.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
425.3.u.e 425.u 17.e $96$ $11.580$ None 85.3.q.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
425.3.u.f 425.u 17.e $128$ $11.580$ None 85.3.p.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{3}^{\mathrm{old}}(425, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(425, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)