Properties

Label 48.16.c
Level $48$
Weight $16$
Character orbit 48.c
Rep. character $\chi_{48}(47,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $4$
Sturm bound $128$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 48.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(128\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(48, [\chi])\).

Total New Old
Modular forms 126 30 96
Cusp forms 114 30 84
Eisenstein series 12 0 12

Trace form

\( 30 q + 11436150 q^{9} + O(q^{10}) \) \( 30 q + 11436150 q^{9} - 124527276 q^{13} + 21870145380 q^{21} - 108901554042 q^{25} + 289110092544 q^{33} - 1598417564220 q^{37} + 9546654693888 q^{45} - 9465219985782 q^{49} - 32870482914900 q^{57} + 69587316369396 q^{61} - 195043768791552 q^{69} - 39888066927924 q^{73} + 369475419109806 q^{81} - 1149787594156032 q^{85} + 439577395080372 q^{93} - 143519349689892 q^{97} + O(q^{100}) \)

Decomposition of \(S_{16}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.16.c.a 48.c 12.b $2$ $68.493$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 48.16.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-3^{5}\zeta_{6}q^{3}+267902\zeta_{6}q^{7}-3^{15}q^{9}+\cdots\)
48.16.c.b 48.c 12.b $4$ $68.493$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 48.16.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-17\beta _{2})q^{3}+5\beta _{3}q^{5}-10213\beta _{2}q^{7}+\cdots\)
48.16.c.c 48.c 12.b $4$ $68.493$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 48.16.c.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{3}-13\beta _{3}q^{5}+203\beta _{1}q^{7}+\cdots\)
48.16.c.d 48.c 12.b $20$ $68.493$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 48.16.c.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-46\beta _{1}+4\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{16}^{\mathrm{old}}(48, [\chi]) \simeq \) \(S_{16}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)