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Properties

Label 350.7.n
Level $350$
Weight $7$
Character orbit 350.n
Rep. character $\chi_{350}(41,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $480$
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.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(420\)

Dimensions

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

Total New Old
Modular forms 1456 480 976
Cusp forms 1424 480 944
Eisenstein series 32 0 32

Trace form

\( 480 q - 3840 q^{4} - 696 q^{7} + 29160 q^{9} + O(q^{10}) \) \( 480 q - 3840 q^{4} - 696 q^{7} + 29160 q^{9} - 6720 q^{11} + 26360 q^{15} - 122880 q^{16} - 2432 q^{18} - 9120 q^{21} + 21408 q^{22} - 20448 q^{23} + 28200 q^{25} + 10368 q^{28} - 14880 q^{29} + 109120 q^{30} + 225860 q^{35} + 933120 q^{36} - 124416 q^{37} - 133160 q^{39} - 149600 q^{42} + 596352 q^{43} + 143360 q^{44} + 246240 q^{46} + 196920 q^{49} - 364800 q^{50} + 623280 q^{51} - 619392 q^{53} + 469744 q^{57} + 1140864 q^{58} - 459520 q^{60} - 2146480 q^{63} - 3932160 q^{64} - 1138600 q^{65} + 1328832 q^{67} + 1052400 q^{70} - 306080 q^{71} - 77824 q^{72} - 507520 q^{74} - 3687672 q^{77} - 2097920 q^{78} + 1130880 q^{79} - 10666400 q^{81} + 437760 q^{84} - 4453920 q^{85} + 530880 q^{86} - 313344 q^{88} - 2037600 q^{91} + 985344 q^{92} - 2314816 q^{93} + 3119800 q^{95} + 5260352 q^{98} - 2222720 q^{99} + O(q^{100}) \)

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

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