Properties

Label 825.2.c
Level $825$
Weight $2$
Character orbit 825.c
Rep. character $\chi_{825}(199,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $7$
Sturm bound $240$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(240\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

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

Total New Old
Modular forms 132 28 104
Cusp forms 108 28 80
Eisenstein series 24 0 24

Trace form

\( 28q - 32q^{4} + 8q^{6} - 28q^{9} + O(q^{10}) \) \( 28q - 32q^{4} + 8q^{6} - 28q^{9} + 8q^{14} + 56q^{16} - 12q^{19} - 4q^{21} - 24q^{24} - 8q^{26} + 32q^{29} + 4q^{31} + 40q^{34} + 32q^{36} + 4q^{39} - 32q^{41} - 16q^{44} - 24q^{46} - 24q^{49} + 16q^{51} - 8q^{54} - 72q^{56} - 32q^{59} + 12q^{61} - 40q^{64} - 8q^{66} - 16q^{69} + 96q^{71} - 40q^{74} + 72q^{76} - 16q^{79} + 28q^{81} + 48q^{84} + 72q^{86} + 56q^{89} - 28q^{91} - 8q^{94} - 24q^{96} + O(q^{100}) \)

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.c.a \(2\) \(6.588\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}+q^{4}-q^{6}+4iq^{7}+\cdots\)
825.2.c.b \(2\) \(6.588\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+2q^{4}-iq^{7}-q^{9}-q^{11}+\cdots\)
825.2.c.c \(4\) \(6.588\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{3}q^{6}+\cdots\)
825.2.c.d \(4\) \(6.588\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
825.2.c.e \(4\) \(6.588\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
825.2.c.f \(6\) \(6.588\) 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{4})q^{2}-\beta _{3}q^{3}+(-3-\beta _{1}+\cdots)q^{4}+\cdots\)
825.2.c.g \(6\) \(6.588\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)