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Properties

Label 197.14.b
Level $197$
Weight $14$
Character orbit 197.b
Rep. character $\chi_{197}(196,\cdot)$
Character field $\Q$
Dimension $214$
Sturm bound $231$

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Defining parameters

Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 197.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 197 \)
Character field: \(\Q\)
Sturm bound: \(231\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(197, [\chi])\).

Total New Old
Modular forms 216 216 0
Cusp forms 214 214 0
Eisenstein series 2 2 0

Trace form

\( 214 q - 893656 q^{4} + 332672 q^{6} - 67294 q^{7} - 113728376 q^{9} + O(q^{10}) \) \( 214 q - 893656 q^{4} + 332672 q^{6} - 67294 q^{7} - 113728376 q^{9} + 3523282 q^{10} + 7757518 q^{15} + 3604811296 q^{16} - 395740478 q^{19} - 763614146 q^{22} + 1052318424 q^{23} - 5620225406 q^{24} - 52154544430 q^{25} - 3239020996 q^{26} + 6130709020 q^{28} + 2114344080 q^{29} - 23994009572 q^{33} + 8509506660 q^{34} + 553392353132 q^{36} + 10351509982 q^{37} - 90250173610 q^{39} - 47178873760 q^{40} - 22990614226 q^{41} - 165158680150 q^{42} - 239701828298 q^{43} - 83122955374 q^{47} + 3185939980900 q^{49} + 310157192058 q^{51} + 122512727586 q^{53} - 1160733050310 q^{54} + 230861537590 q^{55} + 1487721766942 q^{59} - 3639915556126 q^{60} - 321031598902 q^{61} - 2693878517898 q^{62} + 2237036763606 q^{63} - 18524284969978 q^{64} - 3112581399454 q^{65} + 2250605653178 q^{70} + 5622787882616 q^{76} + 55859609437866 q^{81} - 6121089521840 q^{83} - 9479571327172 q^{85} + 17277537358042 q^{88} - 27751312039254 q^{90} - 40296139448732 q^{92} - 13167068181622 q^{93} + 52056667644566 q^{96} + 17116416908958 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(197, [\chi])\) into newform subspaces

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