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Properties

Label 6.15.b
Level $6$
Weight $15$
Character orbit 6.b
Rep. character $\chi_{6}(5,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 6.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(6, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 12 4 8
Eisenstein series 4 0 4

Trace form

\( 4 q - 3276 q^{3} - 32768 q^{4} + 239616 q^{6} - 1654072 q^{7} - 2153628 q^{9} + O(q^{10}) \) \( 4 q - 3276 q^{3} - 32768 q^{4} + 239616 q^{6} - 1654072 q^{7} - 2153628 q^{9} - 11735040 q^{10} + 26836992 q^{12} - 248212120 q^{13} + 520179840 q^{15} + 268435456 q^{16} + 908070912 q^{18} - 1252067608 q^{19} - 2512164312 q^{21} + 2708779008 q^{22} - 1962934272 q^{24} - 1010496860 q^{25} - 18844787052 q^{27} + 13550157824 q^{28} - 22159872000 q^{30} + 48544485512 q^{31} + 126848191104 q^{33} - 73181085696 q^{34} + 17642520576 q^{36} - 229361099608 q^{37} + 176113271880 q^{39} + 96133447680 q^{40} - 532172648448 q^{42} - 475123816024 q^{43} + 78358129920 q^{45} + 1407078998016 q^{46} - 219848638464 q^{48} + 546417874380 q^{49} + 330389632512 q^{51} + 2033353687040 q^{52} - 3372586813440 q^{54} - 6195118383360 q^{55} + 6429522003912 q^{57} + 3954244177920 q^{58} - 4261313249280 q^{60} - 8008506933784 q^{61} + 13558362184584 q^{63} - 2199023255552 q^{64} - 12945338929152 q^{66} - 5706498189208 q^{67} + 6766877922048 q^{69} + 26012049530880 q^{70} - 7438916911104 q^{72} + 28135799923400 q^{73} - 21928288537260 q^{75} + 10256937844736 q^{76} - 17912213729280 q^{78} - 80292052723192 q^{79} + 35435631821508 q^{81} + 12944796721152 q^{82} + 20579650043904 q^{84} - 16204620119040 q^{85} - 46328672200320 q^{87} - 22190317633536 q^{88} + 110399597015040 q^{90} + 120737034068560 q^{91} + 53737779031272 q^{93} - 219496277852160 q^{94} + 16080357556224 q^{96} + 178244166574856 q^{97} - 158408610377472 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(6, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
6.15.b.a 6.b 3.b $4$ $7.460$ \(\Q(\sqrt{-2}, \sqrt{-35})\) None \(0\) \(-3276\) \(0\) \(-1654072\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-819-7\beta _{1}-\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{15}^{\mathrm{old}}(6, [\chi])\) into lower level spaces

\( S_{15}^{\mathrm{old}}(6, [\chi]) \cong \) \(S_{15}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)