Properties

Label 192.8.k
Level $192$
Weight $8$
Character orbit 192.k
Rep. character $\chi_{192}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $108$
Sturm bound $256$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 192.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(256\)

Dimensions

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

Total New Old
Modular forms 464 116 348
Cusp forms 432 108 324
Eisenstein series 32 8 24

Trace form

\( 108 q + 2 q^{3} + 8 q^{7} + O(q^{10}) \) \( 108 q + 2 q^{3} + 8 q^{7} - 4 q^{13} + 60588 q^{19} - 4376 q^{21} - 238042 q^{27} - 4 q^{33} - 4 q^{37} + 283948 q^{39} - 752844 q^{43} - 156252 q^{45} + 9882508 q^{49} - 1121592 q^{51} - 4191000 q^{55} - 2279892 q^{61} - 1552540 q^{67} + 4372 q^{69} + 886066 q^{75} - 4 q^{81} + 7846496 q^{85} + 40789116 q^{87} + 1590680 q^{91} - 14495396 q^{93} - 8 q^{97} + 4701076 q^{99} + O(q^{100}) \)

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

The newforms in this space have not yet been added to the LMFDB.

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

\( S_{8}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)