Properties

Label 48.11.e
Level $48$
Weight $11$
Character orbit 48.e
Rep. character $\chi_{48}(17,\cdot)$
Character field $\Q$
Dimension $19$
Newform subspaces $5$
Sturm bound $88$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 48.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(88\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(48, [\chi])\).

Total New Old
Modular forms 86 21 65
Cusp forms 74 19 55
Eisenstein series 12 2 10

Trace form

\( 19 q + q^{3} + 14634 q^{7} + 10603 q^{9} + O(q^{10}) \) \( 19 q + q^{3} + 14634 q^{7} + 10603 q^{9} - 2 q^{13} + 979168 q^{15} + 4870498 q^{19} - 3012690 q^{21} - 22092229 q^{25} + 2496745 q^{27} - 9985094 q^{31} - 11413216 q^{33} + 92157774 q^{37} - 48282422 q^{39} - 116402638 q^{43} + 149890624 q^{45} + 133604777 q^{49} - 81908608 q^{51} - 38443456 q^{55} - 524597738 q^{57} - 1530816482 q^{61} + 199417338 q^{63} + 1718224258 q^{67} - 630246976 q^{69} + 2366968150 q^{73} + 355081529 q^{75} + 723935834 q^{79} + 577607491 q^{81} + 5304494336 q^{85} - 5040791904 q^{87} - 5362682076 q^{91} + 2508968926 q^{93} + 2003876966 q^{97} - 6841367104 q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.11.e.a $1$ $30.497$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(243\) \(0\) \(-22082\) \(q+3^{5}q^{3}-22082q^{7}+3^{10}q^{9}+702218q^{13}+\cdots\)
48.11.e.b $2$ $30.497$ \(\Q(\sqrt{-35}) \) None \(0\) \(-234\) \(0\) \(20636\) \(q+(-117+\beta )q^{3}-6\beta q^{5}+10318q^{7}+\cdots\)
48.11.e.c $2$ $30.497$ \(\Q(\sqrt{-5}) \) None \(0\) \(54\) \(0\) \(-34468\) \(q+(3^{3}+9\beta )q^{3}+106\beta q^{5}-17234q^{7}+\cdots\)
48.11.e.d $4$ $30.497$ \(\Q(\sqrt{-2}, \sqrt{85})\) None \(0\) \(-84\) \(0\) \(45112\) \(q+(-21-\beta _{1})q^{3}+(4\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
48.11.e.e $10$ $30.497$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(22\) \(0\) \(5436\) \(q+(2-\beta _{1})q^{3}+(\beta _{1}-\beta _{3})q^{5}+(545+7\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)