↑

Properties

Label 192.8.j
Level $192$
Weight $8$
Character orbit 192.j
Rep. character $\chi_{192}(49,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $1$
Sturm bound $256$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 192.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(256\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(192, [\chi])\).

Total New Old
Modular forms 464 56 408
Cusp forms 432 56 376
Eisenstein series 32 0 32

Trace form

\( 56 q + O(q^{10}) \) \( 56 q + 2408 q^{11} - 27000 q^{15} + 60584 q^{19} + 103376 q^{29} + 714984 q^{31} - 816504 q^{35} - 831152 q^{37} + 386664 q^{43} - 6588344 q^{49} + 1496664 q^{51} - 1815632 q^{53} - 1835936 q^{59} - 2279888 q^{61} + 2000376 q^{63} + 2853776 q^{65} - 9576368 q^{67} + 4790448 q^{69} + 5630256 q^{75} - 11914448 q^{77} - 19459688 q^{79} - 29760696 q^{81} - 503480 q^{83} - 7534000 q^{85} + 177640 q^{91} - 64673232 q^{95} + 1755432 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.8.j.a 192.j 16.e $56$ $59.978$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{8}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)