Properties

Label 26.6.b
Level $26$
Weight $6$
Character orbit 26.b
Rep. character $\chi_{26}(25,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $21$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 26 = 2 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 26.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(21\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(26, [\chi])\).

Total New Old
Modular forms 20 4 16
Cusp forms 16 4 12
Eisenstein series 4 0 4

Trace form

\( 4 q - 18 q^{3} - 64 q^{4} - 602 q^{9} + O(q^{10}) \) \( 4 q - 18 q^{3} - 64 q^{4} - 602 q^{9} - 136 q^{10} + 288 q^{12} - 182 q^{13} + 184 q^{14} + 1024 q^{16} + 1274 q^{17} - 2160 q^{22} + 6308 q^{23} - 1950 q^{25} + 3640 q^{26} + 4482 q^{27} - 11588 q^{29} - 7480 q^{30} - 21862 q^{35} + 9632 q^{36} - 768 q^{38} + 19604 q^{39} + 2176 q^{40} - 13544 q^{42} - 13842 q^{43} - 4608 q^{48} + 31730 q^{49} + 42530 q^{51} + 2912 q^{52} + 74928 q^{53} - 65280 q^{55} - 2944 q^{56} - 126756 q^{61} + 88432 q^{62} - 16384 q^{64} + 34034 q^{65} - 24960 q^{66} - 20384 q^{68} - 10468 q^{69} - 1144 q^{74} - 25616 q^{75} - 89160 q^{77} - 1352 q^{78} + 35684 q^{79} + 24100 q^{81} - 129920 q^{82} + 93184 q^{87} + 34560 q^{88} + 93296 q^{90} + 30862 q^{91} - 100928 q^{92} + 177720 q^{94} + 265404 q^{95} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(26, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
26.6.b.a 26.b 13.b $2$ $4.170$ \(\Q(\sqrt{-1}) \) None 26.6.b.a \(0\) \(-26\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{2}-13q^{3}-2^{4}q^{4}-51iq^{5}+\cdots\)
26.6.b.b 26.b 13.b $2$ $4.170$ \(\Q(\sqrt{-1}) \) None 26.6.b.b \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+4q^{3}-2^{4}q^{4}+34iq^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(26, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(26, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)