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Properties

Label 192.4.r
Level $192$
Weight $4$
Character orbit 192.r
Rep. character $\chi_{192}(13,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $384$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 192.r (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(192, [\chi])\).

Total New Old
Modular forms 784 384 400
Cusp forms 752 384 368
Eisenstein series 32 0 32

Trace form

\( 384 q + O(q^{10}) \) \( 384 q - 944 q^{22} + 80 q^{26} + 1520 q^{28} + 2480 q^{32} + 2000 q^{34} - 880 q^{38} - 3280 q^{40} - 2000 q^{44} + 5712 q^{50} - 2976 q^{51} + 3312 q^{52} + 432 q^{54} - 576 q^{55} - 784 q^{56} + 5504 q^{59} - 4896 q^{60} - 5856 q^{62} + 2016 q^{63} - 6048 q^{64} - 5472 q^{66} + 1632 q^{67} - 4128 q^{68} - 2016 q^{70} + 896 q^{71} + 5264 q^{74} - 4416 q^{75} + 1488 q^{76} + 7056 q^{78} - 5664 q^{79} + 10032 q^{80} - 6960 q^{82} + 3120 q^{88} + 8928 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.4.r.a 192.r 64.i $384$ $11.328$ None 192.4.r.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{4}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(192, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)