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

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

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.c.a 825.c 5.b $2$ $6.588$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}-q^{6}+4iq^{7}+\cdots\)
825.2.c.b 825.c 5.b $2$ $6.588$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2q^{4}-iq^{7}-q^{9}-q^{11}+\cdots\)
825.2.c.c 825.c 5.b $4$ $6.588$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{3}q^{6}+\cdots\)
825.2.c.d 825.c 5.b $4$ $6.588$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
825.2.c.e 825.c 5.b $4$ $6.588$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
825.2.c.f 825.c 5.b $6$ $6.588$ 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}+\beta _{4})q^{2}-\beta _{3}q^{3}+(-3-\beta _{1}+\cdots)q^{4}+\cdots\)
825.2.c.g 825.c 5.b $6$ $6.588$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)

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

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