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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 $3$

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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
230.4.g.a 230.g 23.c $50$ $13.570$ None \(-10\) \(-5\) \(25\) \(-19\) $\mathrm{SU}(2)[C_{11}]$
230.4.g.b 230.g 23.c $60$ $13.570$ None \(12\) \(-3\) \(-30\) \(100\) $\mathrm{SU}(2)[C_{11}]$
230.4.g.c 230.g 23.c $60$ $13.570$ None \(12\) \(5\) \(30\) \(-3\) $\mathrm{SU}(2)[C_{11}]$
230.4.g.d 230.g 23.c $70$ $13.570$ None \(-14\) \(3\) \(-35\) \(-78\) $\mathrm{SU}(2)[C_{11}]$

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

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