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Properties

Label 825.2.o
Level $825$
Weight $2$
Character orbit 825.o
Rep. character $\chi_{825}(421,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $240$
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.o (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
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 496 240 256
Cusp forms 464 240 224
Eisenstein series 32 0 32

Trace form

\( 240 q - 60 q^{4} + 6 q^{5} + 16 q^{6} - 6 q^{7} - 60 q^{9} + O(q^{10}) \) \( 240 q - 60 q^{4} + 6 q^{5} + 16 q^{6} - 6 q^{7} - 60 q^{9} + 8 q^{10} - 4 q^{11} + 4 q^{12} - 8 q^{13} + 12 q^{15} - 56 q^{16} + 12 q^{17} - 24 q^{19} + 4 q^{20} - 8 q^{21} + 8 q^{23} - 12 q^{24} - 8 q^{25} - 40 q^{26} - 26 q^{28} + 4 q^{30} + 2 q^{31} - 40 q^{32} - 16 q^{33} - 2 q^{35} + 240 q^{36} + 60 q^{37} + 84 q^{38} - 16 q^{39} - 44 q^{40} + 6 q^{41} + 2 q^{42} + 52 q^{43} + 26 q^{44} - 4 q^{45} + 48 q^{46} - 24 q^{47} + 8 q^{48} - 62 q^{49} + 6 q^{50} - 16 q^{51} - 48 q^{52} - 24 q^{53} - 4 q^{54} + 34 q^{55} + 8 q^{57} - 28 q^{58} - 24 q^{59} - 40 q^{60} - 28 q^{61} - 120 q^{62} - 6 q^{63} - 76 q^{64} + 36 q^{65} - 8 q^{66} - 56 q^{67} + 74 q^{68} + 2 q^{69} - 44 q^{70} + 16 q^{71} - 56 q^{73} + 22 q^{74} - 12 q^{75} + 168 q^{76} - 66 q^{77} - 24 q^{78} + 172 q^{79} - 2 q^{80} - 60 q^{81} - 24 q^{82} - 136 q^{83} + 96 q^{84} + 16 q^{85} + 72 q^{86} + 20 q^{87} - 44 q^{88} - 2 q^{90} + 30 q^{91} - 60 q^{92} + 72 q^{93} + 56 q^{94} + 130 q^{95} - 28 q^{96} - 120 q^{97} - 124 q^{98} - 4 q^{99} + O(q^{100}) \)

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.o.a 825.o 275.j $4$ $6.588$ \(\Q(\zeta_{10})\) None \(0\) \(-1\) \(5\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{3}q^{3}+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{4}+\cdots\)
825.2.o.b 825.o 275.j $4$ $6.588$ \(\Q(\zeta_{10})\) None \(3\) \(1\) \(5\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)
825.2.o.c 825.o 275.j $116$ $6.588$ None \(-2\) \(-29\) \(-1\) \(-13\) $\mathrm{SU}(2)[C_{5}]$
825.2.o.d 825.o 275.j $116$ $6.588$ None \(-1\) \(29\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{5}]$

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

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