Properties

Label 230.4.g
Level $230$
Weight $4$
Character orbit 230.g
Rep. character $\chi_{230}(31,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $240$
Newform subspaces $4$
Sturm bound $144$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 230.g (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(230, [\chi])\).

Total New Old
Modular forms 1120 240 880
Cusp forms 1040 240 800
Eisenstein series 80 0 80

Trace form

\( 240q - 96q^{4} - 10q^{5} - 8q^{6} - 188q^{9} + O(q^{10}) \) \( 240q - 96q^{4} - 10q^{5} - 8q^{6} - 188q^{9} - 20q^{10} - 108q^{11} - 32q^{13} + 96q^{14} - 384q^{16} - 552q^{17} - 224q^{18} + 428q^{19} - 40q^{20} + 2184q^{21} + 880q^{22} - 132q^{23} - 32q^{24} - 600q^{25} + 672q^{26} - 408q^{27} - 1284q^{29} + 160q^{30} - 2064q^{31} + 424q^{33} - 624q^{34} - 1210q^{35} - 752q^{36} - 132q^{37} - 520q^{38} - 1100q^{39} - 80q^{40} + 2284q^{41} - 128q^{42} + 2636q^{43} - 432q^{44} + 2600q^{45} - 264q^{46} + 1320q^{47} + 154q^{49} + 456q^{51} - 128q^{52} - 56q^{53} - 3732q^{54} - 2100q^{55} - 1552q^{56} - 11616q^{57} - 3104q^{58} - 5346q^{59} - 236q^{61} + 3112q^{62} + 9824q^{63} - 1536q^{64} - 700q^{65} + 6688q^{66} + 6276q^{67} + 5184q^{68} + 1056q^{69} + 360q^{70} - 584q^{71} + 4032q^{72} + 3560q^{73} + 5144q^{74} - 48q^{76} + 928q^{77} - 1320q^{78} - 4892q^{79} - 160q^{80} - 4024q^{81} - 7920q^{82} - 14816q^{83} - 5608q^{84} + 560q^{85} - 2044q^{86} + 11548q^{87} - 352q^{88} + 5044q^{89} - 740q^{90} + 568q^{91} - 528q^{92} + 8064q^{93} + 960q^{94} + 960q^{95} - 128q^{96} + 508q^{97} + 2112q^{98} + 6280q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(230, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
230.4.g.a \(50\) \(13.570\) None \(-10\) \(-5\) \(25\) \(-19\)
230.4.g.b \(60\) \(13.570\) None \(12\) \(-3\) \(-30\) \(100\)
230.4.g.c \(60\) \(13.570\) None \(12\) \(5\) \(30\) \(-3\)
230.4.g.d \(70\) \(13.570\) None \(-14\) \(3\) \(-35\) \(-78\)

Decomposition of \(S_{4}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(230, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)