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Properties

Label 825.2.bl
Level $825$
Weight $2$
Character orbit 825.bl
Rep. character $\chi_{825}(34,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $208$
Newform subspaces $2$
Sturm bound $240$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.bl (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 496 208 288
Cusp forms 464 208 256
Eisenstein series 32 0 32

Trace form

\( 208 q + 56 q^{4} - 4 q^{5} + 60 q^{8} + 52 q^{9} + O(q^{10}) \) \( 208 q + 56 q^{4} - 4 q^{5} + 60 q^{8} + 52 q^{9} - 12 q^{10} + 24 q^{14} - 64 q^{16} - 44 q^{20} - 40 q^{23} + 4 q^{25} + 16 q^{26} - 32 q^{29} + 64 q^{30} - 24 q^{31} + 72 q^{34} - 56 q^{36} + 20 q^{37} - 60 q^{38} + 28 q^{40} - 8 q^{41} + 4 q^{45} - 40 q^{46} - 272 q^{49} - 188 q^{50} - 80 q^{52} - 20 q^{53} + 60 q^{58} - 48 q^{59} + 8 q^{60} + 8 q^{61} + 68 q^{64} + 100 q^{65} - 8 q^{66} + 120 q^{67} + 16 q^{69} - 24 q^{70} + 60 q^{72} + 40 q^{73} + 16 q^{74} - 24 q^{76} - 8 q^{79} + 52 q^{80} - 52 q^{81} + 60 q^{83} - 48 q^{84} + 20 q^{85} + 60 q^{86} - 60 q^{88} - 36 q^{89} - 48 q^{90} - 12 q^{91} + 80 q^{92} + 12 q^{94} - 72 q^{95} + 80 q^{96} + 60 q^{97} + O(q^{100}) \)

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.bl.a 825.bl 25.e $104$ $6.588$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{10}]$
825.2.bl.b 825.bl 25.e $104$ $6.588$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)