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Properties

Label 825.2.j
Level $825$
Weight $2$
Character orbit 825.j
Rep. character $\chi_{825}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $4$
Sturm bound $240$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(240\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(825, [\chi])\).

Total New Old
Modular forms 264 72 192
Cusp forms 216 72 144
Eisenstein series 48 0 48

Trace form

\( 72 q + O(q^{10}) \) \( 72 q + 16 q^{11} - 16 q^{12} - 104 q^{16} - 32 q^{22} + 32 q^{23} + 32 q^{31} - 16 q^{33} - 72 q^{36} + 8 q^{37} + 56 q^{38} - 8 q^{42} - 32 q^{48} - 24 q^{53} - 80 q^{56} + 24 q^{58} + 32 q^{66} + 32 q^{67} + 64 q^{71} - 24 q^{77} + 24 q^{78} - 72 q^{81} + 72 q^{82} + 80 q^{86} - 104 q^{88} + 32 q^{91} - 80 q^{92} + 48 q^{93} - 88 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
825.2.j.a 825.j 55.e $8$ $6.588$ \(\Q(\zeta_{24})\) None \(-4\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{24}^{2}q^{2}-\zeta_{24}q^{3}+(-1+\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
825.2.j.b 825.j 55.e $8$ $6.588$ \(\Q(\zeta_{24})\) None \(4\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\zeta_{24}^{2}+\zeta_{24}^{3})q^{2}-\zeta_{24}q^{3}+\cdots\)
825.2.j.c 825.j 55.e $24$ $6.588$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
825.2.j.d 825.j 55.e $32$ $6.588$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)