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Properties

Label 162.7.f
Level $162$
Weight $7$
Character orbit 162.f
Rep. character $\chi_{162}(17,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $108$
Sturm bound $189$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 162.f (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(189\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(162, [\chi])\).

Total New Old
Modular forms 1008 108 900
Cusp forms 936 108 828
Eisenstein series 72 0 72

Trace form

\( 108 q + 432 q^{5} + O(q^{10}) \) \( 108 q + 432 q^{5} + 378 q^{11} - 4752 q^{14} - 27648 q^{20} + 10800 q^{22} + 59832 q^{23} + 31968 q^{25} - 155628 q^{29} - 36720 q^{31} + 82080 q^{34} + 536544 q^{35} - 245808 q^{38} + 56646 q^{41} - 148770 q^{43} + 721872 q^{47} + 311256 q^{49} + 311040 q^{50} - 152064 q^{56} - 856116 q^{59} + 51408 q^{61} + 1769472 q^{64} + 4448952 q^{65} + 1608822 q^{67} + 252288 q^{68} + 1188000 q^{70} - 855360 q^{71} + 514080 q^{73} + 856224 q^{74} - 915840 q^{76} + 6362280 q^{77} - 1325376 q^{79} - 3439260 q^{83} + 4968000 q^{85} - 1530576 q^{86} + 691200 q^{88} + 964710 q^{89} + 902880 q^{91} + 525312 q^{92} - 4421088 q^{94} + 1857708 q^{95} - 286578 q^{97} - 4393440 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

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

Decomposition of \(S_{7}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(162, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)