# Properties

 Label 74.3.d Level $74$ Weight $3$ Character orbit 74.d Rep. character $\chi_{74}(31,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $10$ Newform subspaces $4$ Sturm bound $28$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$74 = 2 \cdot 37$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 74.d (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$37$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$28$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$3$$, $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(74, [\chi])$$.

Total New Old
Modular forms 42 10 32
Cusp forms 34 10 24
Eisenstein series 8 0 8

## Trace form

 $$10 q + 2 q^{2} - 6 q^{5} - 4 q^{8} + 34 q^{9} + O(q^{10})$$ $$10 q + 2 q^{2} - 6 q^{5} - 4 q^{8} + 34 q^{9} + 12 q^{10} - 16 q^{12} - 6 q^{13} + 16 q^{14} - 12 q^{15} - 40 q^{16} + 10 q^{17} - 30 q^{18} + 24 q^{19} - 12 q^{20} + 16 q^{22} - 52 q^{23} + 44 q^{26} - 62 q^{29} - 100 q^{31} - 8 q^{32} - 48 q^{33} - 36 q^{34} + 76 q^{35} + 28 q^{37} + 8 q^{38} + 100 q^{39} + 32 q^{42} - 64 q^{43} - 186 q^{45} + 136 q^{46} + 328 q^{47} - 114 q^{49} + 18 q^{50} + 244 q^{51} - 12 q^{52} + 64 q^{53} + 72 q^{54} - 76 q^{55} - 32 q^{56} + 116 q^{57} - 244 q^{59} + 24 q^{60} - 126 q^{61} + 72 q^{63} - 32 q^{66} + 20 q^{68} - 88 q^{69} - 416 q^{70} + 48 q^{71} + 60 q^{72} + 266 q^{74} + 128 q^{75} + 48 q^{76} + 32 q^{79} + 24 q^{80} - 22 q^{81} - 116 q^{82} - 184 q^{83} + 96 q^{84} + 24 q^{86} + 248 q^{87} + 32 q^{88} - 474 q^{89} - 180 q^{90} + 188 q^{91} - 104 q^{92} - 48 q^{93} + 16 q^{94} - 134 q^{97} - 274 q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(74, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
74.3.d.a $$2$$ $$2.016$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$-12$$ $$10$$ $$q+(1+i)q^{2}+iq^{3}+2iq^{4}+(-6+6i)q^{5}+\cdots$$
74.3.d.b $$2$$ $$2.016$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$6$$ $$-8$$ $$q+(1+i)q^{2}+4iq^{3}+2iq^{4}+(3-3i)q^{5}+\cdots$$
74.3.d.c $$2$$ $$2.016$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$6$$ $$6$$ $$q+(1+i)q^{2}-3iq^{3}+2iq^{4}+(3-3i)q^{5}+\cdots$$
74.3.d.d $$4$$ $$2.016$$ $$\Q(i, \sqrt{65})$$ None $$-4$$ $$0$$ $$-6$$ $$-8$$ $$q+(-1+\beta _{1})q^{2}-\beta _{1}q^{3}-2\beta _{1}q^{4}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(74, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(74, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(37, [\chi])$$$$^{\oplus 2}$$