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Properties

Label 304.7.r
Level $304$
Weight $7$
Character orbit 304.r
Rep. character $\chi_{304}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $118$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 304.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(304, [\chi])\).

Total New Old
Modular forms 492 122 370
Cusp forms 468 118 350
Eisenstein series 24 4 20

Trace form

\( 118 q + 3 q^{3} - q^{5} - 716 q^{7} + 13390 q^{9} + O(q^{10}) \) \( 118 q + 3 q^{3} - q^{5} - 716 q^{7} + 13390 q^{9} + 4 q^{11} - 3 q^{13} + 3 q^{15} - 6841 q^{17} + 8114 q^{19} - 2190 q^{21} - 8903 q^{23} - 171876 q^{25} - 3 q^{29} - 6210 q^{33} + 39722 q^{35} - 134618 q^{39} + 121329 q^{41} + 87361 q^{43} + 29788 q^{45} + 62833 q^{47} + 1815234 q^{49} + 120531 q^{51} + 182277 q^{53} - 397870 q^{55} + 367285 q^{57} + 3 q^{59} + 238295 q^{61} + 354620 q^{63} + 1116291 q^{67} + 780123 q^{71} - 306541 q^{73} - 711640 q^{77} - 2339061 q^{79} - 2392051 q^{81} - 1691244 q^{83} - 108047 q^{85} + 4857750 q^{87} - 1812819 q^{89} + 1430070 q^{91} + 1330424 q^{93} - 2628199 q^{95} + 1016817 q^{97} + 2025572 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

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

Decomposition of \(S_{7}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)