# 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

## 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

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

## 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

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