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

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

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

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