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Properties

Label 196.4.i
Level $196$
Weight $4$
Character orbit 196.i
Rep. character $\chi_{196}(29,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $84$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 196.i (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(196, [\chi])\).

Total New Old
Modular forms 522 84 438
Cusp forms 486 84 402
Eisenstein series 36 0 36

Trace form

\( 84 q + 6 q^{3} + 2 q^{5} - 56 q^{9} + O(q^{10}) \) \( 84 q + 6 q^{3} + 2 q^{5} - 56 q^{9} - 42 q^{11} + 94 q^{13} + 126 q^{15} - 136 q^{17} - 360 q^{19} - 98 q^{21} + 238 q^{23} - 154 q^{25} + 654 q^{27} - 182 q^{29} - 140 q^{31} - 352 q^{33} + 812 q^{35} + 70 q^{37} + 490 q^{39} + 128 q^{41} - 476 q^{43} + 146 q^{45} + 344 q^{47} + 1246 q^{49} + 672 q^{51} - 952 q^{53} - 3440 q^{55} - 2100 q^{57} + 236 q^{59} + 1152 q^{61} + 2226 q^{63} + 700 q^{67} - 3324 q^{69} - 1778 q^{71} + 2052 q^{73} + 4366 q^{75} + 896 q^{77} + 1148 q^{79} - 56 q^{81} + 3434 q^{83} - 252 q^{85} + 2442 q^{87} - 2832 q^{89} - 7140 q^{91} - 4900 q^{93} - 4480 q^{95} - 568 q^{97} + 13048 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(196, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
196.4.i.a 196.i 49.e $84$ $11.564$ None \(0\) \(6\) \(2\) \(0\) $\mathrm{SU}(2)[C_{7}]$

Decomposition of \(S_{4}^{\mathrm{old}}(196, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(196, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)