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Properties

Label 10.11.c
Level $10$
Weight $11$
Character orbit 10.c
Rep. character $\chi_{10}(3,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $10$
Newform subspaces $3$
Sturm bound $16$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 10.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(16\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(10, [\chi])\).

Total New Old
Modular forms 34 10 24
Cusp forms 26 10 16
Eisenstein series 8 0 8

Trace form

\( 10 q - 32 q^{2} - 124 q^{3} + 7560 q^{5} - 12160 q^{6} + 10604 q^{7} + 16384 q^{8} + O(q^{10}) \) \( 10 q - 32 q^{2} - 124 q^{3} + 7560 q^{5} - 12160 q^{6} + 10604 q^{7} + 16384 q^{8} - 94880 q^{10} + 451520 q^{11} - 63488 q^{12} - 988434 q^{13} + 3637820 q^{15} - 2621440 q^{16} - 52906 q^{17} - 7111648 q^{18} + 4183040 q^{20} + 20016320 q^{21} - 13506304 q^{22} - 26934364 q^{23} + 51867350 q^{25} + 15915840 q^{26} - 53985640 q^{27} - 5429248 q^{28} + 12272640 q^{30} + 75553720 q^{31} + 8388608 q^{32} - 100984528 q^{33} - 194072740 q^{35} + 136186880 q^{36} + 78377634 q^{37} + 146994560 q^{38} + 6471680 q^{40} - 407745280 q^{41} - 72606464 q^{42} + 291961716 q^{43} - 329257430 q^{45} + 101491840 q^{46} + 877618884 q^{47} + 32505856 q^{48} - 1147160800 q^{50} + 663858520 q^{51} - 506078208 q^{52} + 59690386 q^{53} + 955263120 q^{55} + 269025280 q^{56} - 395251120 q^{57} + 468378880 q^{58} - 166942720 q^{60} + 709135920 q^{61} - 3714249344 q^{62} - 5999298844 q^{63} + 4317976170 q^{65} + 7842145280 q^{66} + 2285641604 q^{67} + 27087872 q^{68} - 1659966080 q^{70} - 7725259880 q^{71} - 3641163776 q^{72} - 4474810454 q^{73} + 8638494700 q^{75} + 5823385600 q^{76} + 4559799088 q^{77} + 14413532544 q^{78} - 1981808640 q^{80} - 23040515690 q^{81} - 13760829184 q^{82} - 7763146644 q^{83} - 1500700690 q^{85} + 13415015040 q^{86} + 44300553440 q^{87} + 6915227648 q^{88} - 32944166560 q^{90} - 32840264280 q^{91} - 13790394368 q^{92} + 22411006592 q^{93} + 3342839800 q^{95} + 3187671040 q^{96} + 30947240394 q^{97} + 23335064288 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(10, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
10.11.c.a 10.c 5.c $2$ $6.354$ \(\Q(\sqrt{-1}) \) None \(32\) \(-366\) \(-3750\) \(-16814\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2^{4}+2^{4}i)q^{2}+(-183+183i)q^{3}+\cdots\)
10.11.c.b 10.c 5.c $2$ $6.354$ \(\Q(\sqrt{-1}) \) None \(32\) \(114\) \(5850\) \(13906\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2^{4}+2^{4}i)q^{2}+(57-57i)q^{3}+2^{9}iq^{4}+\cdots\)
10.11.c.c 10.c 5.c $6$ $6.354$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-96\) \(128\) \(5460\) \(13512\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2^{4}-2^{4}\beta _{1})q^{2}+(21-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(10, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)