Properties

Label 425.2.b
Level $425$
Weight $2$
Character orbit 425.b
Rep. character $\chi_{425}(324,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $6$
Sturm bound $90$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 425 = 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 425.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(90\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(425, [\chi])\).

Total New Old
Modular forms 52 24 28
Cusp forms 40 24 16
Eisenstein series 12 0 12

Trace form

\( 24 q - 24 q^{4} - 4 q^{6} - 20 q^{9} + O(q^{10}) \) \( 24 q - 24 q^{4} - 4 q^{6} - 20 q^{9} - 4 q^{14} + 40 q^{16} - 28 q^{21} + 16 q^{24} - 20 q^{26} + 4 q^{29} + 36 q^{31} - 4 q^{34} + 4 q^{36} - 56 q^{39} - 4 q^{41} + 24 q^{44} + 28 q^{46} - 4 q^{49} + 8 q^{51} + 80 q^{54} - 8 q^{56} - 8 q^{59} - 16 q^{61} - 104 q^{64} - 96 q^{66} + 56 q^{71} + 68 q^{74} + 32 q^{76} - 68 q^{79} + 24 q^{81} + 140 q^{84} - 64 q^{86} + 56 q^{89} + 64 q^{94} - 156 q^{96} - 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(425, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
425.2.b.a 425.b 5.b $2$ $3.394$ \(\Q(\sqrt{-1}) \) None 425.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}-q^{6}+iq^{7}+3iq^{8}+\cdots\)
425.2.b.b 425.b 5.b $2$ $3.394$ \(\Q(\sqrt{-1}) \) None 17.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}-4iq^{7}+3iq^{8}+3q^{9}+\cdots\)
425.2.b.c 425.b 5.b $2$ $3.394$ \(\Q(\sqrt{-1}) \) None 85.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2iq^{3}+q^{4}+2q^{6}-2iq^{7}+\cdots\)
425.2.b.d 425.b 5.b $4$ $3.394$ \(\Q(\zeta_{12})\) None 85.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
425.2.b.e 425.b 5.b $4$ $3.394$ \(\Q(\zeta_{8})\) None 85.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-2\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots\)
425.2.b.f 425.b 5.b $10$ $3.394$ 10.0.\(\cdots\).1 None 425.2.a.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{8}q^{2}+\beta _{6}q^{3}+(-2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(425, [\chi])\) into lower level spaces

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