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Properties

Label 350.7.s
Level $350$
Weight $7$
Character orbit 350.s
Rep. character $\chi_{350}(113,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $720$
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.s (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(420\)

Dimensions

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

Total New Old
Modular forms 2912 720 2192
Cusp forms 2848 720 2128
Eisenstein series 64 0 64

Trace form

\( 720 q + 16 q^{2} - 128 q^{3} - 88 q^{5} - 512 q^{8} + O(q^{10}) \) \( 720 q + 16 q^{2} - 128 q^{3} - 88 q^{5} - 512 q^{8} + 1872 q^{10} - 4096 q^{12} - 9228 q^{13} + 928 q^{15} + 184320 q^{16} + 7332 q^{17} - 75328 q^{18} - 76800 q^{19} - 12800 q^{20} + 71424 q^{22} + 118576 q^{23} - 192636 q^{25} + 65120 q^{26} - 413504 q^{27} - 49600 q^{29} + 62208 q^{30} + 65536 q^{32} + 462752 q^{33} + 66000 q^{34} - 1399680 q^{36} + 312132 q^{37} - 22464 q^{38} - 414800 q^{39} - 99840 q^{40} + 217120 q^{41} - 21504 q^{43} + 709204 q^{45} + 1328032 q^{47} + 131072 q^{48} - 479632 q^{50} - 295296 q^{52} - 91324 q^{53} - 1796352 q^{55} + 557104 q^{57} + 388608 q^{58} + 4780800 q^{59} + 1075712 q^{60} - 776880 q^{61} - 31232 q^{62} - 417088 q^{63} - 3701572 q^{65} + 2020224 q^{67} - 234624 q^{68} + 197568 q^{70} - 3035520 q^{71} + 699904 q^{72} + 606012 q^{73} - 1137920 q^{75} - 570752 q^{77} - 10658112 q^{78} - 9158400 q^{79} + 90112 q^{80} + 14105300 q^{81} + 610176 q^{82} - 1606608 q^{83} + 803640 q^{85} + 8863248 q^{87} + 571392 q^{88} - 183700 q^{89} - 429616 q^{90} - 6138368 q^{92} - 10354032 q^{93} + 8149744 q^{95} + 596508 q^{97} - 268912 q^{98} + O(q^{100}) \)

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

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