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Properties

Label 192.3.i
Level $192$
Weight $3$
Character orbit 192.i
Rep. character $\chi_{192}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $28$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 192.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(192, [\chi])\).

Total New Old
Modular forms 144 36 108
Cusp forms 112 28 84
Eisenstein series 32 8 24

Trace form

\( 28 q + 2 q^{3} - 4 q^{13} + 4 q^{15} + 36 q^{19} + 16 q^{21} + 50 q^{27} + 8 q^{31} - 4 q^{33} - 4 q^{37} + 68 q^{43} - 52 q^{45} - 36 q^{49} - 96 q^{51} - 36 q^{61} - 192 q^{63} - 124 q^{67} - 20 q^{69}+ \cdots + 292 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.3.i.a 192.i 48.i $8$ $5.232$ 8.0.629407744.1 None 48.3.i.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
192.3.i.b 192.i 48.i $20$ $5.232$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 48.3.i.b \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{3}+(\beta _{8}-\beta _{9}-\beta _{10})q^{5}-\beta _{6}q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(192, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)