Properties

Label 825.2.f
Level $825$
Weight $2$
Character orbit 825.f
Rep. character $\chi_{825}(626,\cdot)$
Character field $\Q$
Dimension $70$
Newform subspaces $7$
Sturm bound $240$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(240\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(23\), \(37\)

Dimensions

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

Total New Old
Modular forms 132 82 50
Cusp forms 108 70 38
Eisenstein series 24 12 12

Trace form

\( 70 q + 3 q^{3} + 68 q^{4} - 7 q^{9} + O(q^{10}) \) \( 70 q + 3 q^{3} + 68 q^{4} - 7 q^{9} + 14 q^{12} + 56 q^{16} + 8 q^{22} - 12 q^{27} - 34 q^{31} + 7 q^{33} + 8 q^{34} - 58 q^{36} - 2 q^{37} + 8 q^{42} + 48 q^{48} - 46 q^{49} - 8 q^{58} + 40 q^{64} - 84 q^{66} - 62 q^{67} + 89 q^{69} - 88 q^{78} - 63 q^{81} + 56 q^{82} - 16 q^{88} + 16 q^{91} + 51 q^{93} + 14 q^{97} + 3 q^{99} + O(q^{100}) \)

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.f.a $2$ $6.588$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(-1\) \(0\) \(0\) \(q-\beta q^{3}-2q^{4}+(-3+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
825.2.f.b $4$ $6.588$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-2q^{4}+(3+\beta _{2})q^{9}+(1+2\beta _{2}+\cdots)q^{11}+\cdots\)
825.2.f.c $8$ $6.588$ 8.0.619810816.2 None \(0\) \(2\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{4})q^{2}+(-\beta _{3}-\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots\)
825.2.f.d $8$ $6.588$ 8.0.619810816.2 None \(0\) \(2\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{4})q^{2}-\beta _{4}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
825.2.f.e $16$ $6.588$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{3}q^{2}+\beta _{4}q^{3}+(1+\beta _{1})q^{4}+\beta _{5}q^{6}+\cdots\)
825.2.f.f $16$ $6.588$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}-\beta _{5}q^{3}+(2-\beta _{2})q^{4}+\beta _{14}q^{6}+\cdots\)
825.2.f.g $16$ $6.588$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(1+\beta _{1})q^{4}-\beta _{5}q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)