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Properties

Label 176.9.r
Level $176$
Weight $9$
Character orbit 176.r
Rep. character $\chi_{176}(15,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $192$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 176 = 2^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 176.r (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(176, [\chi])\).

Total New Old
Modular forms 792 192 600
Cusp forms 744 192 552
Eisenstein series 48 0 48

Trace form

\( 192 q + 116400 q^{9} + O(q^{10}) \) \( 192 q + 116400 q^{9} - 82656 q^{17} - 1837872 q^{25} - 4339536 q^{33} - 11160000 q^{41} + 27624576 q^{45} + 29003568 q^{49} - 27050976 q^{53} - 15257424 q^{57} - 569664 q^{61} - 54360000 q^{65} - 71659296 q^{69} + 302770944 q^{73} - 234982368 q^{77} - 185503008 q^{81} + 380937600 q^{85} - 507586464 q^{89} + 100557600 q^{93} + 594381264 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(176, [\chi])\) into newform subspaces

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

Decomposition of \(S_{9}^{\mathrm{old}}(176, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(176, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)