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Properties

Label 75.6.i
Level $75$
Weight $6$
Character orbit 75.i
Rep. character $\chi_{75}(4,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $96$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 75.i (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(75, [\chi])\).

Total New Old
Modular forms 208 96 112
Cusp forms 192 96 96
Eisenstein series 16 0 16

Trace form

\( 96 q + 352 q^{4} - 120 q^{5} + 72 q^{6} - 1230 q^{8} + 1944 q^{9} + O(q^{10}) \) \( 96 q + 352 q^{4} - 120 q^{5} + 72 q^{6} - 1230 q^{8} + 1944 q^{9} - 890 q^{10} + 474 q^{11} + 2748 q^{14} - 780 q^{16} + 1910 q^{17} - 5522 q^{19} - 19220 q^{20} + 1764 q^{21} + 6170 q^{22} + 21980 q^{23} + 13824 q^{24} + 11790 q^{25} - 11028 q^{26} - 9120 q^{28} - 24304 q^{29} - 22860 q^{30} + 1566 q^{31} - 3690 q^{33} + 24224 q^{34} + 10250 q^{35} - 28512 q^{36} + 16490 q^{37} + 68730 q^{38} - 12168 q^{39} - 106480 q^{40} + 26126 q^{41} - 43560 q^{42} - 10814 q^{44} + 9720 q^{45} + 22956 q^{46} + 66440 q^{47} - 123480 q^{49} + 329620 q^{50} - 83232 q^{51} + 251240 q^{52} - 91690 q^{53} - 5832 q^{54} - 123470 q^{55} + 116100 q^{56} - 483290 q^{58} - 97428 q^{59} + 119610 q^{60} + 91560 q^{61} - 138410 q^{62} + 47790 q^{63} + 127738 q^{64} - 235130 q^{65} + 118296 q^{66} + 163960 q^{67} - 73332 q^{69} + 209520 q^{70} + 155672 q^{71} - 99630 q^{72} + 18980 q^{73} + 100588 q^{74} - 464032 q^{76} + 119560 q^{77} - 112020 q^{79} - 66300 q^{80} - 157464 q^{81} + 148010 q^{83} - 61128 q^{84} + 346980 q^{85} - 295956 q^{86} - 371160 q^{87} - 189090 q^{88} - 494082 q^{89} - 144180 q^{90} - 79494 q^{91} + 599810 q^{92} + 234622 q^{94} + 605800 q^{95} + 210744 q^{96} + 372140 q^{97} + 891060 q^{98} + 25596 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(75, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
75.6.i.a 75.i 25.e $96$ $12.029$ None \(0\) \(0\) \(-120\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{6}^{\mathrm{old}}(75, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(75, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)