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Properties

Label 114.4.e
Level $114$
Weight $4$
Character orbit 114.e
Rep. character $\chi_{114}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $5$
Sturm bound $80$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 114.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(80\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(114, [\chi])\).

Total New Old
Modular forms 128 20 108
Cusp forms 112 20 92
Eisenstein series 16 0 16

Trace form

\( 20 q + 6 q^{3} - 40 q^{4} - 16 q^{5} + 12 q^{7} - 90 q^{9} + O(q^{10}) \) \( 20 q + 6 q^{3} - 40 q^{4} - 16 q^{5} + 12 q^{7} - 90 q^{9} - 40 q^{10} - 168 q^{11} - 48 q^{12} - 174 q^{13} - 88 q^{14} + 24 q^{15} - 160 q^{16} + 196 q^{17} + 120 q^{19} + 128 q^{20} - 78 q^{21} - 72 q^{22} - 12 q^{23} + 42 q^{25} - 688 q^{26} - 108 q^{27} - 24 q^{28} + 52 q^{29} + 48 q^{30} + 188 q^{31} - 324 q^{33} - 152 q^{34} + 336 q^{35} - 360 q^{36} + 1060 q^{37} - 272 q^{38} + 252 q^{39} - 160 q^{40} + 248 q^{41} + 24 q^{42} + 170 q^{43} + 336 q^{44} + 288 q^{45} + 576 q^{46} + 324 q^{47} + 96 q^{48} + 440 q^{49} - 320 q^{50} - 204 q^{51} - 696 q^{52} + 1996 q^{53} + 2080 q^{55} + 704 q^{56} - 870 q^{57} + 1456 q^{58} - 488 q^{59} + 96 q^{60} + 310 q^{61} - 248 q^{62} - 54 q^{63} + 1280 q^{64} - 1328 q^{65} - 120 q^{66} + 34 q^{67} - 1568 q^{68} + 2952 q^{69} - 1128 q^{70} - 848 q^{71} - 66 q^{73} - 264 q^{74} - 2004 q^{75} - 744 q^{76} + 3256 q^{77} + 24 q^{78} - 2470 q^{79} - 256 q^{80} - 810 q^{81} + 752 q^{82} - 4456 q^{83} + 624 q^{84} - 864 q^{85} - 944 q^{86} - 1320 q^{87} + 576 q^{88} - 2456 q^{89} - 360 q^{90} - 106 q^{91} - 48 q^{92} - 294 q^{93} + 5952 q^{94} + 2608 q^{95} - 1260 q^{97} + 4592 q^{98} + 756 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(114, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
114.4.e.a 114.e 19.c $2$ $6.726$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-2\) \(-42\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
114.4.e.b 114.e 19.c $2$ $6.726$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(6\) \(38\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
114.4.e.c 114.e 19.c $4$ $6.726$ \(\Q(\sqrt{-3}, \sqrt{-10})\) None \(-4\) \(-6\) \(-8\) \(36\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{1}q^{2}-3\beta _{1}q^{3}+(-4+4\beta _{1})q^{4}+\cdots\)
114.4.e.d 114.e 19.c $6$ $6.726$ 6.0.627014547.1 None \(-6\) \(9\) \(-10\) \(14\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{1}q^{2}+3\beta _{1}q^{3}+(-4+4\beta _{1})q^{4}+\cdots\)
114.4.e.e 114.e 19.c $6$ $6.726$ 6.0.6967728.1 None \(6\) \(9\) \(-2\) \(-34\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{3})q^{2}+(3+3\beta _{3})q^{3}+4\beta _{3}q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(114, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(114, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)