Degree 4 L-functions, examples (reviewed)

Examples of primitive degree 4 L-functions are:

• $L(s, f, \mathrm{sym}^3)$: the symmetric cube L-function of a cusp form on GL(2)

• $L(s, F, \mathrm{spin})$: spin L-function of a Siegel modular form on GSp(4) (genus 2)

• $L(s,f)$: standard L-function of a cusp form on the Picard group SL(2,Z[i])

• $L(s,f)$: standard L-function of a cusp form on Sp(4)

• $L(s,f)$: standard L-function of a cusp form on GL(4)

• $L(s,E)$: L-function of an elliptic curve over a quadratic field

• $L(s,f)$: standard L-function of a Hilbert modular form on GL(2) over a real quadratic field