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Properties

Label 1197.4.v
Level $1197$
Weight $4$
Character orbit 1197.v
Rep. character $\chi_{1197}(145,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $396$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1197.v (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1197, [\chi])\).

Total New Old
Modular forms 976 404 572
Cusp forms 944 396 548
Eisenstein series 32 8 24

Trace form

\( 396 q - 1570 q^{4} + 4 q^{7} + O(q^{10}) \) \( 396 q - 1570 q^{4} + 4 q^{7} - 24 q^{10} + 30 q^{11} - 66 q^{13} + 78 q^{14} + 6158 q^{16} - 63 q^{17} + 303 q^{19} - 282 q^{22} + 123 q^{23} - 9526 q^{25} + 813 q^{26} - 217 q^{28} + 192 q^{29} - 30 q^{31} + 360 q^{34} - 18 q^{35} + 642 q^{37} - 636 q^{38} + 936 q^{40} + 666 q^{41} - 70 q^{43} - 666 q^{44} - 540 q^{46} - 135 q^{47} - 134 q^{49} + 405 q^{52} + 1443 q^{55} - 2349 q^{56} - 1553 q^{58} + 1245 q^{59} - 849 q^{61} - 501 q^{62} - 22190 q^{64} + 813 q^{65} - 453 q^{68} - 1032 q^{70} + 2064 q^{71} - 2505 q^{73} - 639 q^{74} - 3630 q^{76} - 792 q^{77} + 2190 q^{82} + 2166 q^{85} - 3156 q^{86} + 4644 q^{88} + 3 q^{89} - 3912 q^{91} - 4284 q^{92} + 264 q^{94} - 5115 q^{95} - 2052 q^{97} - 6081 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1197, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1197, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1197, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 2}\)