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Properties

Label 350.7.f
Level $350$
Weight $7$
Character orbit 350.f
Rep. character $\chi_{350}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $108$
Sturm bound $420$

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Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 350.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Sturm bound: \(420\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(350, [\chi])\).

Total New Old
Modular forms 744 108 636
Cusp forms 696 108 588
Eisenstein series 48 0 48

Trace form

\( 108 q + 16 q^{2} - 128 q^{3} - 512 q^{8} + O(q^{10}) \) \( 108 q + 16 q^{2} - 128 q^{3} - 512 q^{8} - 2304 q^{11} - 4096 q^{12} - 9228 q^{13} - 110592 q^{16} + 7332 q^{17} + 21872 q^{18} - 43904 q^{21} - 17856 q^{22} + 58736 q^{23} - 65120 q^{26} + 53056 q^{27} + 153792 q^{31} - 16384 q^{32} - 159328 q^{33} + 946304 q^{36} - 111588 q^{37} - 22464 q^{38} - 917536 q^{41} - 21504 q^{43} + 340992 q^{46} + 385472 q^{47} + 131072 q^{48} - 487568 q^{51} - 295296 q^{52} + 120316 q^{53} + 557104 q^{57} + 388608 q^{58} - 91728 q^{61} - 31232 q^{62} + 104272 q^{63} - 26368 q^{66} - 1044096 q^{67} - 234624 q^{68} + 3324704 q^{71} + 699904 q^{72} - 1905348 q^{73} - 570752 q^{77} + 154688 q^{78} - 5817420 q^{81} + 610176 q^{82} - 1606608 q^{83} + 2690944 q^{86} - 4348912 q^{87} + 571392 q^{88} + 3161088 q^{91} + 1879552 q^{92} + 3023488 q^{93} + 596508 q^{97} - 268912 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{7}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(350, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)