Properties

Label 234.4.h
Level $234$
Weight $4$
Character orbit 234.h
Rep. character $\chi_{234}(55,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $34$
Newform subspaces $10$
Sturm bound $168$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 234.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
Sturm bound: \(168\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(234, [\chi])\).

Total New Old
Modular forms 268 34 234
Cusp forms 236 34 202
Eisenstein series 32 0 32

Trace form

\( 34 q - 2 q^{2} - 68 q^{4} - 10 q^{5} - 2 q^{7} + 16 q^{8} + O(q^{10}) \) \( 34 q - 2 q^{2} - 68 q^{4} - 10 q^{5} - 2 q^{7} + 16 q^{8} + 30 q^{10} - 50 q^{11} + 141 q^{13} + 64 q^{14} - 272 q^{16} - 33 q^{17} + 266 q^{19} + 20 q^{20} + 16 q^{22} + 50 q^{23} + 764 q^{25} + 230 q^{26} - 8 q^{28} - 313 q^{29} - 552 q^{31} - 32 q^{32} + 212 q^{34} - 4 q^{35} + 737 q^{37} + 576 q^{38} - 240 q^{40} + 75 q^{41} + 58 q^{43} + 400 q^{44} - 344 q^{46} - 2192 q^{47} - 1863 q^{49} - 760 q^{50} - 336 q^{52} + 4014 q^{53} + 528 q^{55} - 128 q^{56} + 190 q^{58} - 454 q^{59} + 817 q^{61} - 464 q^{62} + 2176 q^{64} - 2351 q^{65} - 2154 q^{67} - 132 q^{68} - 2736 q^{70} + 466 q^{71} + 2450 q^{73} - 678 q^{74} + 1064 q^{76} + 7324 q^{77} + 800 q^{79} + 80 q^{80} - 178 q^{82} + 2064 q^{83} - 4387 q^{85} - 2768 q^{86} + 64 q^{88} - 4668 q^{89} + 5034 q^{91} - 400 q^{92} - 680 q^{94} - 4608 q^{95} - 216 q^{97} - 1842 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(234, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
234.4.h.a 234.h 13.c $2$ $13.806$ \(\Q(\sqrt{-3}) \) None 234.4.h.a \(-2\) \(0\) \(-8\) \(23\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-4q^{5}+\cdots\)
234.4.h.b 234.h 13.c $2$ $13.806$ \(\Q(\sqrt{-3}) \) None 26.4.c.a \(-2\) \(0\) \(-4\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-2q^{5}+\cdots\)
234.4.h.c 234.h 13.c $2$ $13.806$ \(\Q(\sqrt{-3}) \) None 78.4.e.a \(2\) \(0\) \(-14\) \(-16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-7q^{5}-2^{4}\zeta_{6}q^{7}+\cdots\)
234.4.h.d 234.h 13.c $2$ $13.806$ \(\Q(\sqrt{-3}) \) None 234.4.h.a \(2\) \(0\) \(8\) \(23\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+4q^{5}+23\zeta_{6}q^{7}+\cdots\)
234.4.h.e 234.h 13.c $4$ $13.806$ \(\Q(\sqrt{-3}, \sqrt{142})\) None 234.4.h.e \(-4\) \(0\) \(-28\) \(-36\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+(-7+\beta _{3})q^{5}+\cdots\)
234.4.h.f 234.h 13.c $4$ $13.806$ \(\Q(\sqrt{-3}, \sqrt{61})\) None 78.4.e.c \(-4\) \(0\) \(-4\) \(-18\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\beta _{1})q^{2}-4\beta _{1}q^{4}+(-1+2\beta _{3})q^{5}+\cdots\)
234.4.h.g 234.h 13.c $4$ $13.806$ \(\Q(\sqrt{-3}, \sqrt{673})\) None 78.4.e.b \(4\) \(0\) \(-26\) \(-9\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{2})q^{2}-4\beta _{2}q^{4}+(-7+\beta _{3})q^{5}+\cdots\)
234.4.h.h 234.h 13.c $4$ $13.806$ \(\Q(\sqrt{-3}, \sqrt{217})\) None 26.4.c.b \(4\) \(0\) \(14\) \(45\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{2})q^{2}-4\beta _{2}q^{4}+(3+\beta _{3})q^{5}+\cdots\)
234.4.h.i 234.h 13.c $4$ $13.806$ \(\Q(\sqrt{-3}, \sqrt{142})\) None 234.4.h.e \(4\) \(0\) \(28\) \(-36\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(7+\beta _{3})q^{5}+\cdots\)
234.4.h.j 234.h 13.c $6$ $13.806$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 78.4.e.d \(-6\) \(0\) \(24\) \(17\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(4+\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(234, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(234, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)