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Properties

Label 336.7.x
Level $336$
Weight $7$
Character orbit 336.x
Rep. character $\chi_{336}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 336.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(336, [\chi])\).

Total New Old
Modular forms 776 288 488
Cusp forms 760 288 472
Eisenstein series 16 0 16

Trace form

\( 288 q + 180 q^{4} + O(q^{10}) \) \( 288 q + 180 q^{4} - 3000 q^{10} + 2720 q^{11} + 3888 q^{12} + 6860 q^{14} - 4668 q^{16} - 4860 q^{18} + 7872 q^{19} + 83268 q^{22} - 26240 q^{23} - 36936 q^{24} + 10600 q^{26} - 66400 q^{29} + 66096 q^{30} + 105920 q^{32} - 133536 q^{34} - 64152 q^{36} + 7200 q^{37} - 234136 q^{38} + 575640 q^{40} - 535968 q^{43} + 328740 q^{44} + 182328 q^{46} + 4840416 q^{49} - 1343460 q^{50} - 160704 q^{51} - 249552 q^{52} - 443680 q^{53} - 157464 q^{54} - 465408 q^{55} + 163268 q^{56} + 28860 q^{58} + 627912 q^{60} + 652992 q^{61} + 541680 q^{62} - 475524 q^{64} + 745664 q^{65} - 301920 q^{67} - 4557064 q^{68} - 1083456 q^{69} - 568008 q^{70} - 82620 q^{72} + 4080276 q^{74} + 2146176 q^{75} + 5082744 q^{76} + 932960 q^{77} + 99144 q^{78} - 1510480 q^{80} - 17006112 q^{81} - 6671640 q^{82} + 4995520 q^{83} + 744000 q^{85} - 3551764 q^{86} + 6261396 q^{88} + 1014768 q^{90} + 4447440 q^{92} + 6021576 q^{94} + 1117800 q^{96} + 660960 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

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

Decomposition of \(S_{7}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)