Properties

Label 425.4.b
Level $425$
Weight $4$
Character orbit 425.b
Rep. character $\chi_{425}(324,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $11$
Sturm bound $180$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 425 = 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 425.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(180\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(425, [\chi])\).

Total New Old
Modular forms 140 72 68
Cusp forms 128 72 56
Eisenstein series 12 0 12

Trace form

\( 72 q - 288 q^{4} - 8 q^{6} - 656 q^{9} + O(q^{10}) \) \( 72 q - 288 q^{4} - 8 q^{6} - 656 q^{9} - 32 q^{11} + 172 q^{14} + 1296 q^{16} + 184 q^{19} + 16 q^{21} - 668 q^{24} + 220 q^{26} + 548 q^{29} + 180 q^{31} + 136 q^{34} + 2308 q^{36} - 240 q^{39} - 784 q^{41} + 1908 q^{44} - 1428 q^{46} - 6144 q^{49} - 408 q^{51} - 360 q^{54} - 1160 q^{56} + 48 q^{59} + 44 q^{61} - 7536 q^{64} + 4640 q^{66} + 2344 q^{69} - 2588 q^{71} - 5016 q^{74} + 312 q^{76} + 764 q^{79} + 9384 q^{81} + 1596 q^{84} + 9592 q^{86} - 3288 q^{89} + 2128 q^{91} + 3512 q^{94} + 3496 q^{96} - 3568 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(425, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
425.4.b.a 425.b 5.b $2$ $25.076$ \(\Q(\sqrt{-1}) \) None 85.4.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{2}+7 i q^{3}-q^{4}-21 q^{6}+\cdots\)
425.4.b.b 425.b 5.b $2$ $25.076$ \(\Q(\sqrt{-1}) \) None 85.4.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{2}+5 i q^{3}-q^{4}-15 q^{6}+\cdots\)
425.4.b.c 425.b 5.b $2$ $25.076$ \(\Q(\sqrt{-1}) \) None 17.4.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{2}-8 i q^{3}-q^{4}+24 q^{6}+\cdots\)
425.4.b.d 425.b 5.b $2$ $25.076$ \(\Q(\sqrt{-1}) \) None 85.4.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{2}-10 i q^{3}-q^{4}+30 q^{6}+\cdots\)
425.4.b.e 425.b 5.b $4$ $25.076$ \(\Q(\zeta_{12})\) None 85.4.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta_{2}+2\beta_1)q^{2}+(-\beta_{2}-\beta_1)q^{3}+\cdots\)
425.4.b.f 425.b 5.b $6$ $25.076$ 6.0.27793984.1 None 17.4.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}+2\beta _{4}-2\beta _{5})q^{3}+\cdots\)
425.4.b.g 425.b 5.b $6$ $25.076$ 6.0.27206656.1 None 85.4.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2\beta _{2}-\beta _{4})q^{2}+(\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
425.4.b.h 425.b 5.b $6$ $25.076$ 6.0.5161984.1 None 85.4.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}+\beta _{4}+\beta _{5})q^{2}+(-4\beta _{3}-3\beta _{4}+\cdots)q^{3}+\cdots\)
425.4.b.i 425.b 5.b $10$ $25.076$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 85.4.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+\beta _{4}q^{3}+(-6-\beta _{7}+2\beta _{9})q^{4}+\cdots\)
425.4.b.j 425.b 5.b $12$ $25.076$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 425.4.a.j \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{7}-\beta _{8})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
425.4.b.k 425.b 5.b $20$ $25.076$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None 425.4.a.l \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{11}-\beta _{13})q^{3}+(-6+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(425, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(425, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)