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Properties

Label 825.2.q
Level $825$
Weight $2$
Character orbit 825.q
Rep. character $\chi_{825}(166,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $192$
Newform subspaces $4$
Sturm bound $240$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.q (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 4 \)
Sturm bound: \(240\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 496 192 304
Cusp forms 464 192 272
Eisenstein series 32 0 32

Trace form

\( 192 q + 4 q^{2} - 44 q^{4} + 8 q^{5} - 24 q^{8} - 48 q^{9} + O(q^{10}) \) \( 192 q + 4 q^{2} - 44 q^{4} + 8 q^{5} - 24 q^{8} - 48 q^{9} + 16 q^{10} + 16 q^{13} + 24 q^{14} - 36 q^{16} + 32 q^{17} - 16 q^{18} - 68 q^{20} - 24 q^{23} + 24 q^{25} + 24 q^{26} + 56 q^{28} + 8 q^{29} - 64 q^{30} + 24 q^{31} - 64 q^{32} + 12 q^{34} + 48 q^{35} - 44 q^{36} - 24 q^{37} - 4 q^{38} + 72 q^{40} + 48 q^{41} + 40 q^{42} - 112 q^{43} + 8 q^{45} + 40 q^{46} + 48 q^{47} + 32 q^{48} + 128 q^{49} - 96 q^{50} - 128 q^{52} - 96 q^{53} + 36 q^{58} - 48 q^{59} + 32 q^{60} + 32 q^{61} + 72 q^{62} - 32 q^{64} - 88 q^{65} + 8 q^{66} - 56 q^{67} + 72 q^{68} + 16 q^{69} + 96 q^{70} - 24 q^{72} - 8 q^{73} + 56 q^{74} + 16 q^{75} + 24 q^{76} + 56 q^{78} - 8 q^{79} + 136 q^{80} - 48 q^{81} + 48 q^{82} - 4 q^{83} - 48 q^{84} - 40 q^{85} - 60 q^{86} + 24 q^{87} - 36 q^{88} - 96 q^{89} - 44 q^{90} + 12 q^{91} - 104 q^{92} + 16 q^{93} + 52 q^{94} - 112 q^{95} - 40 q^{96} + 20 q^{97} + 92 q^{98} + O(q^{100}) \)

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.q.a 825.q 25.d $48$ $6.588$ None \(-1\) \(-12\) \(2\) \(24\) $\mathrm{SU}(2)[C_{5}]$
825.2.q.b 825.q 25.d $48$ $6.588$ None \(-1\) \(12\) \(2\) \(24\) $\mathrm{SU}(2)[C_{5}]$
825.2.q.c 825.q 25.d $48$ $6.588$ None \(3\) \(-12\) \(2\) \(-24\) $\mathrm{SU}(2)[C_{5}]$
825.2.q.d 825.q 25.d $48$ $6.588$ None \(3\) \(12\) \(2\) \(-24\) $\mathrm{SU}(2)[C_{5}]$

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

\( S_{2}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)