Properties

Label 825.2.r
Level $825$
Weight $2$
Character orbit 825.r
Rep. character $\chi_{825}(31,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $240$
Newform subspaces $3$
Sturm bound $240$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.r (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 3 \)
Sturm bound: \(240\)
Trace bound: \(1\)
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

\( 240q + 240q^{4} - 4q^{5} - 4q^{6} + 4q^{7} - 60q^{9} + O(q^{10}) \) \( 240q + 240q^{4} - 4q^{5} - 4q^{6} + 4q^{7} - 60q^{9} - 2q^{10} - 4q^{11} + 4q^{12} + 12q^{13} - 8q^{15} + 264q^{16} + 2q^{17} + 56q^{19} - 36q^{20} - 8q^{21} - 30q^{22} - 32q^{23} - 12q^{24} + 12q^{25} + 10q^{26} + 14q^{28} - 16q^{30} + 2q^{31} + 60q^{32} - 16q^{33} - 2q^{35} - 60q^{36} + 10q^{37} - 56q^{38} - 16q^{39} - 54q^{40} - 24q^{41} + 2q^{42} - 48q^{43} - 44q^{44} + 6q^{45} - 12q^{46} + 26q^{47} + 8q^{48} - 52q^{49} + 6q^{50} - 16q^{51} + 32q^{52} - 24q^{53} - 4q^{54} - 16q^{55} - 12q^{57} - 88q^{58} - 24q^{59} - 40q^{60} - 18q^{61} - 10q^{62} + 4q^{63} + 264q^{64} - 34q^{65} - 8q^{66} + 44q^{67} - 26q^{68} - 8q^{69} + 36q^{70} - 24q^{71} - 26q^{73} + 22q^{74} + 28q^{75} + 188q^{76} - 86q^{77} - 24q^{78} - 38q^{79} + 8q^{80} - 60q^{81} + 76q^{82} + 164q^{83} - 24q^{84} + 46q^{85} - 88q^{86} - 40q^{87} - 114q^{88} + 8q^{90} - 10q^{91} - 110q^{92} + 72q^{93} - 84q^{94} + 60q^{95} - 28q^{96} + 70q^{97} - 184q^{98} + 6q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
825.2.r.a \(4\) \(6.588\) \(\Q(\zeta_{10})\) None \(0\) \(-1\) \(5\) \(1\) \(q+(-1-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots\)
825.2.r.b \(116\) \(6.588\) None \(8\) \(-29\) \(-1\) \(-3\)
825.2.r.c \(120\) \(6.588\) None \(-8\) \(30\) \(-8\) \(6\)

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

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