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Properties

Label 26.8.c
Level $26$
Weight $8$
Character orbit 26.c
Rep. character $\chi_{26}(3,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $14$
Newform subspaces $2$
Sturm bound $28$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 26 = 2 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 26.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(28\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(26, [\chi])\).

Total New Old
Modular forms 54 14 40
Cusp forms 46 14 32
Eisenstein series 8 0 8

Trace form

\( 14 q + 8 q^{2} - 448 q^{4} - 110 q^{5} + 612 q^{7} - 1024 q^{8} - 3335 q^{9} + O(q^{10}) \) \( 14 q + 8 q^{2} - 448 q^{4} - 110 q^{5} + 612 q^{7} - 1024 q^{8} - 3335 q^{9} + 4888 q^{10} - 11620 q^{11} - 33319 q^{13} - 27328 q^{14} + 3104 q^{15} - 28672 q^{16} + 21579 q^{17} - 113488 q^{18} - 97536 q^{19} + 3520 q^{20} + 345416 q^{21} + 25312 q^{22} + 2572 q^{23} + 339264 q^{25} - 211640 q^{26} + 133920 q^{27} + 39168 q^{28} + 96931 q^{29} - 223616 q^{30} + 51592 q^{31} + 32768 q^{32} + 656540 q^{33} + 560848 q^{34} - 368636 q^{35} - 213440 q^{36} - 95601 q^{37} - 1635840 q^{38} + 1046136 q^{39} - 625664 q^{40} + 855255 q^{41} + 75520 q^{42} - 449256 q^{43} + 1487360 q^{44} - 1501253 q^{45} + 554784 q^{46} - 2560912 q^{47} - 228915 q^{49} + 32992 q^{50} - 8250592 q^{51} + 1329536 q^{52} - 1974654 q^{53} + 1164672 q^{54} - 173468 q^{55} + 874496 q^{56} + 9514040 q^{57} - 714792 q^{58} + 3055012 q^{59} - 397312 q^{60} - 946005 q^{61} + 4772192 q^{62} - 5388564 q^{63} + 3670016 q^{64} - 9946885 q^{65} - 2868224 q^{66} + 7282252 q^{67} + 1381056 q^{68} + 9273828 q^{69} + 10427584 q^{70} - 3528832 q^{71} + 3631616 q^{72} + 6328546 q^{73} - 610632 q^{74} + 27970672 q^{75} - 6242304 q^{76} - 44793976 q^{77} - 5915520 q^{78} - 12571016 q^{79} + 225280 q^{80} + 9167137 q^{81} + 5515768 q^{82} + 23507040 q^{83} - 11053312 q^{84} + 36700549 q^{85} - 11028352 q^{86} - 11990280 q^{87} + 1619968 q^{88} - 8841162 q^{89} - 49688560 q^{90} - 7985016 q^{91} - 329216 q^{92} + 2034720 q^{93} + 1056448 q^{94} - 13012128 q^{95} - 9478914 q^{97} + 9653448 q^{98} - 23827928 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(26, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
26.8.c.a 26.c 13.c $6$ $8.122$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 26.8.c.a \(-24\) \(0\) \(-666\) \(1160\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-8-8\beta _{3})q^{2}-\beta _{1}q^{3}+2^{6}\beta _{3}q^{4}+\cdots\)
26.8.c.b 26.c 13.c $8$ $8.122$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 26.8.c.b \(32\) \(0\) \(556\) \(-548\) $\mathrm{SU}(2)[C_{3}]$ \(q-8\beta _{1}q^{2}+\beta _{3}q^{3}+(-2^{6}-2^{6}\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(26, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(26, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)