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Properties

Label 350.7.p
Level $350$
Weight $7$
Character orbit 350.p
Rep. character $\chi_{350}(93,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $288$
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.p (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(420\)

Dimensions

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

Total New Old
Modular forms 1488 288 1200
Cusp forms 1392 288 1104
Eisenstein series 96 0 96

Trace form

\( 288 q + 896 q^{6} - 696 q^{7} + O(q^{10}) \) \( 288 q + 896 q^{6} - 696 q^{7} - 5552 q^{11} + 147456 q^{16} - 8512 q^{17} + 2432 q^{18} + 37104 q^{21} + 30336 q^{22} + 2688 q^{23} - 34048 q^{26} - 321552 q^{27} - 5376 q^{28} + 177408 q^{31} + 58184 q^{33} + 2184192 q^{36} - 184032 q^{37} - 68992 q^{38} + 821408 q^{41} + 25408 q^{42} - 14880 q^{43} - 326592 q^{46} - 146720 q^{47} + 336000 q^{51} + 959136 q^{53} - 309248 q^{56} - 429408 q^{57} - 716160 q^{58} + 809088 q^{61} + 485184 q^{62} + 2353936 q^{63} + 931680 q^{67} + 272384 q^{68} + 2831808 q^{71} + 77824 q^{72} - 2092272 q^{73} - 1612800 q^{76} + 2962504 q^{77} - 594176 q^{78} + 10181248 q^{81} - 419328 q^{82} + 2697408 q^{83} + 1715648 q^{86} - 4945528 q^{87} + 485376 q^{88} - 9819456 q^{91} - 172032 q^{92} - 4789968 q^{93} + 458752 q^{96} + 9368688 q^{97} + 6834304 q^{98} + O(q^{100}) \)

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

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